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// SPDX-License-Identifier: MIT

pragma solidity ^0.8.25;

import { IERC20, IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { Ownable } from "@openzeppelin/contracts/access/Ownable.sol";
import { FHERC20 } from "./FHERC20.sol";
import { IWETH } from "./interfaces/IWETH.sol";
import { euint128, FHE } from "@fhenixprotocol/cofhe-contracts/FHE.sol";
import { EnumerableSet } from "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";
import { ConfidentialClaim } from "./ConfidentialClaim.sol";
import { SafeCast } from "@openzeppelin/contracts/utils/math/SafeCast.sol";
import { SafeERC20 } from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

contract ConfidentialETH is FHERC20, Ownable, ConfidentialClaim {
    using EnumerableSet for EnumerableSet.UintSet;
    using SafeERC20 for IERC20;
    using SafeERC20 for IWETH;

    IWETH public wETH;

    constructor(
        IWETH wETH_
    ) Ownable(msg.sender) FHERC20("Confidential Wrapped ETHER", "eETH", IERC20Metadata(address(wETH_)).decimals()) {
        wETH = wETH_;
    }

    /**
     * @dev Returns the address of the erc20 ERC-20 token that is being encrypted wrapped.
     */
    function erc20() public view returns (IERC20) {
        return wETH;
    }

    receive() external payable {}

    fallback() external payable {}

    event EncryptedWETH(address indexed from, address indexed to, uint128 value);
    event EncryptedETH(address indexed from, address indexed to, uint256 value);
    event DecryptedETH(address indexed from, address indexed to, uint128 value);
    event ClaimedDecryptedETH(address indexed from, address indexed to, uint128 value);

    /**
     * @dev The ETH transfer failed.
     */
    error ETHTransferFailed();

    /**
     * @dev The recipient is the zero address.
     */
    error InvalidRecipient();

    function encryptWETH(address to, uint128 value) public {
        if (to == address(0)) to = msg.sender;
        wETH.safeTransferFrom(msg.sender, address(this), value);
        wETH.withdraw(value);
        _mint(to, value);
        emit EncryptedWETH(msg.sender, to, value);
    }

    function encryptETH(address to) public payable {
        if (to == address(0)) to = msg.sender;
        _mint(to, SafeCast.toUint128(msg.value));
        emit EncryptedETH(msg.sender, to, msg.value);
    }

    function decrypt(address to, uint128 value) public {
        if (to == address(0)) to = msg.sender;
        euint128 burned = _burn(msg.sender, value);
        FHE.decrypt(burned);
        _createClaim(to, value, burned);
        emit DecryptedETH(msg.sender, to, value);
    }

    /**
     * @notice Claim a decrypted amount of ETH
     * @param ctHash The ctHash of the burned amount
     */
    function claimDecrypted(uint256 ctHash) public {
        Claim memory claim = _handleClaim(ctHash);

        // Send the ETH to the recipient
        (bool sent, ) = claim.to.call{ value: claim.decryptedAmount }("");
        if (!sent) revert ETHTransferFailed();

        emit ClaimedDecryptedETH(msg.sender, claim.to, claim.decryptedAmount);
    }

    /**
     * @notice Claim all decrypted amounts of ETH
     */
    function claimAllDecrypted() public {
        Claim[] memory claims = _handleClaimAll();

        for (uint256 i = 0; i < claims.length; i++) {
            (bool sent, ) = claims[i].to.call{ value: claims[i].decryptedAmount }("");
            if (!sent) revert ETHTransferFailed();
            emit ClaimedDecryptedETH(msg.sender, claims[i].to, claims[i].decryptedAmount);
        }
    }
}

// SPDX-License-Identifier: BSD-3-Clause-Clear
// solhint-disable one-contract-per-file

pragma solidity >=0.8.19 <0.9.0;

import {Strings} from "@openzeppelin/contracts/utils/Strings.sol";
import {FunctionId, ITaskManager, Utils, EncryptedInput, InEbool, InEuint8, InEuint16, InEuint32, InEuint64, InEuint128, InEuint256, InEaddress} from "./ICofhe.sol";

type ebool is uint256;
type euint8 is uint256;
type euint16 is uint256;
type euint32 is uint256;
type euint64 is uint256;
type euint128 is uint256;
type euint256 is uint256;
type eaddress is uint256;

// ================================
// \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/
// TODO : CHANGE ME AFTER DEPLOYING
// /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\
// ================================
//solhint-disable const-name-snakecase
address constant TASK_MANAGER_ADDRESS = 0xeA30c4B8b44078Bbf8a6ef5b9f1eC1626C7848D9;

library Common {
    error InvalidHexCharacter(bytes1 char);
    error SecurityZoneOutOfBounds(int32 value);

    // Default value for temp hash calculation in unary operations
    string private constant DEFAULT_VALUE = "0";

    function convertInt32ToUint256(int32 value) internal pure returns (uint256) {
        if (value < 0) {
            revert SecurityZoneOutOfBounds(value);
        }
        return uint256(uint32(value));
    }

    function isInitialized(uint256 hash) internal pure returns (bool) {
        return hash != 0;
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(ebool v) internal pure returns (bool) {
        return isInitialized(ebool.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint8 v) internal pure returns (bool) {
        return isInitialized(euint8.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint16 v) internal pure returns (bool) {
        return isInitialized(euint16.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint32 v) internal pure returns (bool) {
        return isInitialized(euint32.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint64 v) internal pure returns (bool) {
        return isInitialized(euint64.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint128 v) internal pure returns (bool) {
        return isInitialized(euint128.unwrap(v));
    }

    // Return true if the encrypted integer is initialized and false otherwise.
    function isInitialized(euint256 v) internal pure returns (bool) {
        return isInitialized(euint256.unwrap(v));
    }

    function isInitialized(eaddress v) internal pure returns (bool) {
        return isInitialized(eaddress.unwrap(v));
    }

    function createUint256Inputs(uint256 input1) internal pure returns (uint256[] memory) {
        uint256[] memory inputs = new uint256[](1);
        inputs[0] = input1;
        return inputs;
    }

    function createUint256Inputs(uint256 input1, uint256 input2) internal pure returns (uint256[] memory) {
        uint256[] memory inputs = new uint256[](2);
        inputs[0] = input1;
        inputs[1] = input2;
        return inputs;
    }

    function createUint256Inputs(uint256 input1, uint256 input2, uint256 input3) internal pure returns (uint256[] memory) {
        uint256[] memory inputs = new uint256[](3);
        inputs[0] = input1;
        inputs[1] = input2;
        inputs[2] = input3;
        return inputs;
    }
}

library Impl {
    function trivialEncrypt(uint256 value, uint8 toType, int32 securityZone) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(toType, FunctionId.trivialEncrypt, new uint256[](0), Common.createUint256Inputs(value, toType, Common.convertInt32ToUint256(securityZone)));
    }

    function cast(uint256 key, uint8 toType) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(toType, FunctionId.cast, Common.createUint256Inputs(key), Common.createUint256Inputs(toType));
    }

    function select(uint8 returnType, ebool control, uint256 ifTrue, uint256 ifFalse) internal returns (uint256 result) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(returnType,
            FunctionId.select,
            Common.createUint256Inputs(ebool.unwrap(control), ifTrue, ifFalse),
            new uint256[](0));
    }

    function mathOp(uint8 returnType, uint256 lhs, uint256 rhs, FunctionId functionId) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(returnType, functionId, Common.createUint256Inputs(lhs, rhs), new uint256[](0));
    }

    function decrypt(uint256 input) internal returns (uint256) {
        ITaskManager(TASK_MANAGER_ADDRESS).createDecryptTask(input, msg.sender);
        return input;
    }

    function getDecryptResult(uint256 input) internal view returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).getDecryptResult(input);
    }

    function getDecryptResultSafe(uint256 input) internal view returns (uint256 result, bool decrypted) {
        return ITaskManager(TASK_MANAGER_ADDRESS).getDecryptResultSafe(input);
    }

    function not(uint8 returnType, uint256 input) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(returnType, FunctionId.not, Common.createUint256Inputs(input), new uint256[](0));
    }

    function square(uint8 returnType, uint256 input) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(returnType, FunctionId.square, Common.createUint256Inputs(input), new uint256[](0));
    }

    function verifyInput(EncryptedInput memory input) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).verifyInput(input, msg.sender);
    }

    /// @notice Generates a random value of a given type with the given seed, for the provided securityZone
    /// @dev Calls the desired function
    /// @param uintType the type of the random value to generate
    /// @param seed the seed to use to create a random value from
    /// @param securityZone the security zone to use for the random value
    function random(uint8 uintType, uint64 seed, int32 securityZone) internal returns (uint256) {
        return ITaskManager(TASK_MANAGER_ADDRESS).createTask(uintType, FunctionId.random, new uint256[](0), Common.createUint256Inputs(seed, Common.convertInt32ToUint256(securityZone)));
    }

    /// @notice Generates a random value of a given type with the given seed
    /// @dev Calls the desired function
    /// @param uintType the type of the random value to generate
    /// @param seed the seed to use to create a random value from
    function random(uint8 uintType, uint32 seed) internal returns (uint256) {
        return random(uintType, seed, 0);
    }

    /// @notice Generates a random value of a given type
    /// @dev Calls the desired function
    /// @param uintType the type of the random value to generate
    function random(uint8 uintType) internal returns (uint256) {
        return random(uintType, 0, 0);
    }

}

library FHE {

    error InvalidEncryptedInput(uint8 got, uint8 expected);
    /// @notice Perform the addition operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the addition result
    function add(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the addition operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the addition result
    function add(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the addition operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the addition result
    function add(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the addition operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the addition result
    function add(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the addition operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the addition result
    function add(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the addition operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted addition
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the addition result
    function add(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.add));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the comparison result
    function lte(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the comparison result
    function lte(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the comparison result
    function lte(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the comparison result
    function lte(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the comparison result
    function lte(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the less than or equal to operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the comparison result
    function lte(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.lte));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the subtraction result
    function sub(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the subtraction result
    function sub(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the subtraction result
    function sub(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the subtraction result
    function sub(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the subtraction result
    function sub(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the subtraction operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted subtraction
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the subtraction result
    function sub(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.sub));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the multiplication result
    function mul(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the multiplication result
    function mul(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the multiplication result
    function mul(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the multiplication result
    function mul(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the multiplication result
    function mul(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the multiplication operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted multiplication
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the multiplication result
    function mul(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.mul));
    }

    /// @notice Perform the less than operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the comparison result
    function lt(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the less than operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the comparison result
    function lt(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the less than operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the comparison result
    function lt(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the less than operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the comparison result
    function lt(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the less than operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the comparison result
    function lt(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the less than operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the comparison result
    function lt(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.lt));
    }

    /// @notice Perform the division operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the division result
    function div(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the division operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the division result
    function div(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the division operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the division result
    function div(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the division operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the division result
    function div(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the division operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the division result
    function div(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the division operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted division
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the division result
    function div(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.div));
    }

    /// @notice Perform the greater than operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the comparison result
    function gt(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the comparison result
    function gt(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the comparison result
    function gt(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the comparison result
    function gt(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the comparison result
    function gt(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the comparison result
    function gt(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.gt));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the comparison result
    function gte(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the comparison result
    function gte(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the comparison result
    function gte(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the comparison result
    function gte(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the comparison result
    function gte(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the greater than or equal to operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the comparison result
    function gte(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.gte));
    }

    /// @notice Perform the remainder operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the remainder result
    function rem(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the remainder operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the remainder result
    function rem(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the remainder operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the remainder result
    function rem(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the remainder operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the remainder result
    function rem(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the remainder operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the remainder result
    function rem(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the remainder operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted remainder calculation
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the remainder result
    function rem(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.rem));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type ebool
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return result of type ebool containing the AND result
    function and(ebool lhs, ebool rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEbool(true);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEbool(true);
        }

        return ebool.wrap(Impl.mathOp(Utils.EBOOL_TFHE, ebool.unwrap(lhs), ebool.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the AND result
    function and(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the AND result
    function and(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the AND result
    function and(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the AND result
    function and(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the AND result
    function and(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise AND operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise AND
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the AND result
    function and(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.and));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type ebool
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return result of type ebool containing the OR result
    function or(ebool lhs, ebool rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEbool(true);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEbool(true);
        }

        return ebool.wrap(Impl.mathOp(Utils.EBOOL_TFHE, ebool.unwrap(lhs), ebool.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the OR result
    function or(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the OR result
    function or(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the OR result
    function or(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the OR result
    function or(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the OR result
    function or(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise OR operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise OR
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the OR result
    function or(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.or));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type ebool
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return result of type ebool containing the XOR result
    function xor(ebool lhs, ebool rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEbool(true);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEbool(true);
        }

        return ebool.wrap(Impl.mathOp(Utils.EBOOL_TFHE, ebool.unwrap(lhs), ebool.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the XOR result
    function xor(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the XOR result
    function xor(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the XOR result
    function xor(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the XOR result
    function xor(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the XOR result
    function xor(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the bitwise XOR operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted bitwise XOR
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the XOR result
    function xor(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.xor));
    }

    /// @notice Perform the equality operation on two parameters of type ebool
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return result of type ebool containing the equality result
    function eq(ebool lhs, ebool rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEbool(true);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEbool(true);
        }

        return ebool.wrap(Impl.mathOp(Utils.EBOOL_TFHE, ebool.unwrap(lhs), ebool.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the equality result
    function eq(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the equality result
    function eq(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the equality result
    function eq(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the equality result
    function eq(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the equality result
    function eq(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the equality result
    function eq(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the equality operation on two parameters of type eaddress
    /// @dev Verifies that inputs are initialized, performs encrypted equality check
    /// @param lhs input of type eaddress
    /// @param rhs second input of type eaddress
    /// @return result of type ebool containing the equality result
    function eq(eaddress lhs, eaddress rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEaddress(address(0));
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEaddress(address(0));
        }

        return ebool.wrap(Impl.mathOp(Utils.EADDRESS_TFHE, eaddress.unwrap(lhs), eaddress.unwrap(rhs), FunctionId.eq));
    }

    /// @notice Perform the inequality operation on two parameters of type ebool
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return result of type ebool containing the inequality result
    function ne(ebool lhs, ebool rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEbool(true);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEbool(true);
        }

        return ebool.wrap(Impl.mathOp(Utils.EBOOL_TFHE, ebool.unwrap(lhs), ebool.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type ebool containing the inequality result
    function ne(euint8 lhs, euint8 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type ebool containing the inequality result
    function ne(euint16 lhs, euint16 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type ebool containing the inequality result
    function ne(euint32 lhs, euint32 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type ebool containing the inequality result
    function ne(euint64 lhs, euint64 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type ebool containing the inequality result
    function ne(euint128 lhs, euint128 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type ebool containing the inequality result
    function ne(euint256 lhs, euint256 rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return ebool.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the inequality operation on two parameters of type eaddress
    /// @dev Verifies that inputs are initialized, performs encrypted inequality check
    /// @param lhs input of type eaddress
    /// @param rhs second input of type eaddress
    /// @return result of type ebool containing the inequality result
    function ne(eaddress lhs, eaddress rhs) internal returns (ebool) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEaddress(address(0));
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEaddress(address(0));
        }

        return ebool.wrap(Impl.mathOp(Utils.EADDRESS_TFHE, eaddress.unwrap(lhs), eaddress.unwrap(rhs), FunctionId.ne));
    }

    /// @notice Perform the minimum operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the minimum value
    function min(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the minimum operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the minimum value
    function min(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the minimum operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the minimum value
    function min(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the minimum operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the minimum value
    function min(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the minimum operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the minimum value
    function min(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the minimum operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted minimum comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the minimum value
    function min(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.min));
    }

    /// @notice Perform the maximum operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted maximum calculation
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the maximum result
    function max(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the maximum operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted maximum calculation
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the maximum result
    function max(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the maximum operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted maximum calculation
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the maximum result
    function max(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the maximum operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted maximum comparison
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the maximum value
    function max(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the maximum operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted maximum comparison
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the maximum value
    function max(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the maximum operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted maximum comparison
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the maximum value
    function max(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.max));
    }

    /// @notice Perform the shift left operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the left shift result
    function shl(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift left operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the left shift result
    function shl(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift left operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the left shift result
    function shl(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift left operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the left shift result
    function shl(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift left operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the left shift result
    function shl(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift left operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted left shift
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the left shift result
    function shl(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.shl));
    }

    /// @notice Perform the shift right operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the right shift result
    function shr(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the shift right operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the right shift result
    function shr(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the shift right operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the right shift result
    function shr(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the shift right operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the right shift result
    function shr(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the shift right operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the right shift result
    function shr(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the shift right operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted right shift
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the right shift result
    function shr(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.shr));
    }

    /// @notice Perform the rol operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the left rotation result
    function rol(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate left operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the left rotation result
    function rol(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate left operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the left rotation result
    function rol(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate left operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the left rotation result
    function rol(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate left operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the left rotation result
    function rol(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate left operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted left rotation
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the left rotation result
    function rol(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.rol));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint8
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return result of type euint8 containing the right rotation result
    function ror(euint8 lhs, euint8 rhs) internal returns (euint8) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint8(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint8(0);
        }

        return euint8.wrap(Impl.mathOp(Utils.EUINT8_TFHE, euint8.unwrap(lhs), euint8.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint16
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return result of type euint16 containing the right rotation result
    function ror(euint16 lhs, euint16 rhs) internal returns (euint16) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint16(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint16(0);
        }

        return euint16.wrap(Impl.mathOp(Utils.EUINT16_TFHE, euint16.unwrap(lhs), euint16.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint32
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return result of type euint32 containing the right rotation result
    function ror(euint32 lhs, euint32 rhs) internal returns (euint32) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint32(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint32(0);
        }

        return euint32.wrap(Impl.mathOp(Utils.EUINT32_TFHE, euint32.unwrap(lhs), euint32.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint64
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return result of type euint64 containing the right rotation result
    function ror(euint64 lhs, euint64 rhs) internal returns (euint64) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint64(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint64(0);
        }

        return euint64.wrap(Impl.mathOp(Utils.EUINT64_TFHE, euint64.unwrap(lhs), euint64.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint128
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return result of type euint128 containing the right rotation result
    function ror(euint128 lhs, euint128 rhs) internal returns (euint128) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint128(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint128(0);
        }

        return euint128.wrap(Impl.mathOp(Utils.EUINT128_TFHE, euint128.unwrap(lhs), euint128.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Perform the rotate right operation on two parameters of type euint256
    /// @dev Verifies that inputs are initialized, performs encrypted right rotation
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return result of type euint256 containing the right rotation result
    function ror(euint256 lhs, euint256 rhs) internal returns (euint256) {
        if (!Common.isInitialized(lhs)) {
            lhs = asEuint256(0);
        }
        if (!Common.isInitialized(rhs)) {
            rhs = asEuint256(0);
        }

        return euint256.wrap(Impl.mathOp(Utils.EUINT256_TFHE, euint256.unwrap(lhs), euint256.unwrap(rhs), FunctionId.ror));
    }

    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(ebool input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }

        ebool.wrap(Impl.decrypt(ebool.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint8 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint8(0);
        }

        euint8.wrap(Impl.decrypt(euint8.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint16 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint16(0);
        }

        euint16.wrap(Impl.decrypt(euint16.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint32 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint32(0);
        }

        euint32.wrap(Impl.decrypt(euint32.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint64 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint64(0);
        }

        euint64.wrap(Impl.decrypt(euint64.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint128 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint128(0);
        }

        euint128.wrap(Impl.decrypt(euint128.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(euint256 input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint256(0);
        }

        euint256.wrap(Impl.decrypt(euint256.unwrap(input1)));
    }
    /// @notice Performs the async decrypt operation on a ciphertext
    /// @dev The decrypted output should be asynchronously handled by the IAsyncFHEReceiver implementation
    /// @param input1 the input ciphertext
    function decrypt(eaddress input1) internal {
        if (!Common.isInitialized(input1)) {
            input1 = asEaddress(address(0));
        }

        Impl.decrypt(eaddress.unwrap(input1));
    }

    /// @notice Gets the decrypted value from a previously decrypted ebool ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The ebool ciphertext to get the decrypted value from
    /// @return The decrypted boolean value
    function getDecryptResult(ebool input1) internal view returns (bool) {
        uint256 result = Impl.getDecryptResult(ebool.unwrap(input1));
        return result != 0;
    }

    /// @notice Gets the decrypted value from a previously decrypted euint8 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint8 ciphertext to get the decrypted value from
    /// @return The decrypted uint8 value
    function getDecryptResult(euint8 input1) internal view returns (uint8) {
        return uint8(Impl.getDecryptResult(euint8.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted euint16 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint16 ciphertext to get the decrypted value from
    /// @return The decrypted uint16 value
    function getDecryptResult(euint16 input1) internal view returns (uint16) {
        return uint16(Impl.getDecryptResult(euint16.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted euint32 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint32 ciphertext to get the decrypted value from
    /// @return The decrypted uint32 value
    function getDecryptResult(euint32 input1) internal view returns (uint32) {
        return uint32(Impl.getDecryptResult(euint32.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted euint64 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint64 ciphertext to get the decrypted value from
    /// @return The decrypted uint64 value
    function getDecryptResult(euint64 input1) internal view returns (uint64) {
        return uint64(Impl.getDecryptResult(euint64.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted euint128 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint128 ciphertext to get the decrypted value from
    /// @return The decrypted uint128 value
    function getDecryptResult(euint128 input1) internal view returns (uint128) {
        return uint128(Impl.getDecryptResult(euint128.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted euint256 ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The euint256 ciphertext to get the decrypted value from
    /// @return The decrypted uint256 value
    function getDecryptResult(euint256 input1) internal view returns (uint256) {
        return uint256(Impl.getDecryptResult(euint256.unwrap(input1)));
    }

    /// @notice Gets the decrypted value from a previously decrypted eaddress ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The eaddress ciphertext to get the decrypted value from
    /// @return The decrypted address value
    function getDecryptResult(eaddress input1) internal view returns (address) {
        return address(uint160(Impl.getDecryptResult(eaddress.unwrap(input1))));
    }

    /// @notice Gets the decrypted value from a previously decrypted raw ciphertext
    /// @dev This function will revert if the ciphertext is not yet decrypted. Use getDecryptResultSafe for a non-reverting version.
    /// @param input1 The raw ciphertext to get the decrypted value from
    /// @return The decrypted uint256 value
    function getDecryptResult(uint256 input1) internal view returns (uint256) {
        return Impl.getDecryptResult(input1);
    }

    /// @notice Safely gets the decrypted value from an ebool ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The ebool ciphertext to get the decrypted value from
    /// @return result The decrypted boolean value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(ebool input1) internal view returns (bool result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(ebool.unwrap(input1));
        return (_result != 0, _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint8 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint8 ciphertext to get the decrypted value from
    /// @return result The decrypted uint8 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint8 input1) internal view returns (uint8 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint8.unwrap(input1));
        return (uint8(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint16 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint16 ciphertext to get the decrypted value from
    /// @return result The decrypted uint16 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint16 input1) internal view returns (uint16 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint16.unwrap(input1));
        return (uint16(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint32 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint32 ciphertext to get the decrypted value from
    /// @return result The decrypted uint32 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint32 input1) internal view returns (uint32 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint32.unwrap(input1));
        return (uint32(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint64 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint64 ciphertext to get the decrypted value from
    /// @return result The decrypted uint64 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint64 input1) internal view returns (uint64 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint64.unwrap(input1));
        return (uint64(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint128 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint128 ciphertext to get the decrypted value from
    /// @return result The decrypted uint128 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint128 input1) internal view returns (uint128 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint128.unwrap(input1));
        return (uint128(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a euint256 ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The euint256 ciphertext to get the decrypted value from
    /// @return result The decrypted uint256 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(euint256 input1) internal view returns (uint256 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(euint256.unwrap(input1));
        return (uint256(_result), _decrypted);
    }

    /// @notice Safely gets the decrypted value from an eaddress ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The eaddress ciphertext to get the decrypted value from
    /// @return result The decrypted address value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(eaddress input1) internal view returns (address result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(eaddress.unwrap(input1));
        return (address(uint160(_result)), _decrypted);
    }

    /// @notice Safely gets the decrypted value from a raw ciphertext
    /// @dev Returns the decrypted value and a flag indicating whether the decryption has finished
    /// @param input1 The raw ciphertext to get the decrypted value from
    /// @return result The decrypted uint256 value
    /// @return decrypted Flag indicating if the value was successfully decrypted
    function getDecryptResultSafe(uint256 input1) internal view returns (uint256 result, bool decrypted) {
        (uint256 _result, bool _decrypted) = Impl.getDecryptResultSafe(input1);
        return (_result, _decrypted);
    }

    /// @notice Performs a multiplexer operation between two ebool values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type ebool
    /// @param input3 Second choice of type ebool
    /// @return result of type ebool containing the selected value
    function select(ebool input1, ebool input2, ebool input3) internal returns (ebool) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEbool(false);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEbool(false);
        }

        return ebool.wrap(Impl.select(Utils.EBOOL_TFHE, input1, ebool.unwrap(input2), ebool.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint8 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint8
    /// @param input3 Second choice of type euint8
    /// @return result of type euint8 containing the selected value
    function select(ebool input1, euint8 input2, euint8 input3) internal returns (euint8) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint8(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint8(0);
        }

        return euint8.wrap(Impl.select(Utils.EUINT8_TFHE, input1, euint8.unwrap(input2), euint8.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint16 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint16
    /// @param input3 Second choice of type euint16
    /// @return result of type euint16 containing the selected value
    function select(ebool input1, euint16 input2, euint16 input3) internal returns (euint16) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint16(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint16(0);
        }

        return euint16.wrap(Impl.select(Utils.EUINT16_TFHE, input1, euint16.unwrap(input2), euint16.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint32 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint32
    /// @param input3 Second choice of type euint32
    /// @return result of type euint32 containing the selected value
    function select(ebool input1, euint32 input2, euint32 input3) internal returns (euint32) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint32(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint32(0);
        }

        return euint32.wrap(Impl.select(Utils.EUINT32_TFHE, input1, euint32.unwrap(input2), euint32.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint64 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint64
    /// @param input3 Second choice of type euint64
    /// @return result of type euint64 containing the selected value
    function select(ebool input1, euint64 input2, euint64 input3) internal returns (euint64) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint64(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint64(0);
        }

        return euint64.wrap(Impl.select(Utils.EUINT64_TFHE, input1, euint64.unwrap(input2), euint64.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint128 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint128
    /// @param input3 Second choice of type euint128
    /// @return result of type euint128 containing the selected value
    function select(ebool input1, euint128 input2, euint128 input3) internal returns (euint128) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint128(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint128(0);
        }

        return euint128.wrap(Impl.select(Utils.EUINT128_TFHE, input1, euint128.unwrap(input2), euint128.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two euint256 values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type euint256
    /// @param input3 Second choice of type euint256
    /// @return result of type euint256 containing the selected value
    function select(ebool input1, euint256 input2, euint256 input3) internal returns (euint256) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEuint256(0);
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEuint256(0);
        }

        return euint256.wrap(Impl.select(Utils.EUINT256_TFHE, input1, euint256.unwrap(input2), euint256.unwrap(input3)));
    }

    /// @notice Performs a multiplexer operation between two eaddress values based on a selector
    /// @dev If input1 is true, returns input2, otherwise returns input3. All inputs are initialized to defaults if not set.
    /// @param input1 The selector of type ebool
    /// @param input2 First choice of type eaddress
    /// @param input3 Second choice of type eaddress
    /// @return result of type eaddress containing the selected value
    function select(ebool input1, eaddress input2, eaddress input3) internal returns (eaddress) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }
        if (!Common.isInitialized(input2)) {
            input2 = asEaddress(address(0));
        }
        if (!Common.isInitialized(input3)) {
            input3 = asEaddress(address(0));
        }

        return eaddress.wrap(Impl.select(Utils.EADDRESS_TFHE, input1, eaddress.unwrap(input2), eaddress.unwrap(input3)));
    }

    /// @notice Performs the not operation on a ciphertext
    /// @dev Verifies that the input value matches a valid ciphertext.
    /// @param input1 the input ciphertext
    function not(ebool input1) internal returns (ebool) {
        if (!Common.isInitialized(input1)) {
            input1 = asEbool(false);
        }

        return ebool.wrap(Impl.not(Utils.EBOOL_TFHE, ebool.unwrap(input1)));
    }

    /// @notice Performs the not operation on a ciphertext
    /// @dev Verifies that the input value matches a valid ciphertext.
    /// @param input1 the input ciphertext
    function not(euint8 input1) internal returns (euint8) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint8(0);
        }

        return euint8.wrap(Impl.not(Utils.EUINT8_TFHE, euint8.unwrap(input1)));
    }
    /// @notice Performs the not operation on a ciphertext
    /// @dev Verifies that the input value matches a valid ciphertext.
    /// @param input1 the input ciphertext
    function not(euint16 input1) internal returns (euint16) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint16(0);
        }

        return euint16.wrap(Impl.not(Utils.EUINT16_TFHE, euint16.unwrap(input1)));
    }
    /// @notice Performs the not operation on a ciphertext
    /// @dev Verifies that the input value matches a valid ciphertext.
    /// @param input1 the input ciphertext
    function not(euint32 input1) internal returns (euint32) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint32(0);
        }

        return euint32.wrap(Impl.not(Utils.EUINT32_TFHE, euint32.unwrap(input1)));
    }

    /// @notice Performs the bitwise NOT operation on an encrypted 64-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      The operation inverts all bits of the input value.
    /// @param input1 The input ciphertext to negate
    /// @return An euint64 containing the bitwise NOT of the input
    function not(euint64 input1) internal returns (euint64) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint64(0);
        }

        return euint64.wrap(Impl.not(Utils.EUINT64_TFHE, euint64.unwrap(input1)));
    }

    /// @notice Performs the bitwise NOT operation on an encrypted 128-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      The operation inverts all bits of the input value.
    /// @param input1 The input ciphertext to negate
    /// @return An euint128 containing the bitwise NOT of the input
    function not(euint128 input1) internal returns (euint128) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint128(0);
        }

        return euint128.wrap(Impl.not(Utils.EUINT128_TFHE, euint128.unwrap(input1)));
    }

    /// @notice Performs the bitwise NOT operation on an encrypted 256-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      The operation inverts all bits of the input value.
    /// @param input1 The input ciphertext to negate
    /// @return An euint256 containing the bitwise NOT of the input
    function not(euint256 input1) internal returns (euint256) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint256(0);
        }

        return euint256.wrap(Impl.not(Utils.EUINT256_TFHE, euint256.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 8-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 8 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint8 containing the square of the input
    function square(euint8 input1) internal returns (euint8) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint8(0);
        }

        return euint8.wrap(Impl.square(Utils.EUINT8_TFHE, euint8.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 16-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 16 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint16 containing the square of the input
    function square(euint16 input1) internal returns (euint16) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint16(0);
        }

        return euint16.wrap(Impl.square(Utils.EUINT16_TFHE, euint16.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 32-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 32 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint32 containing the square of the input
    function square(euint32 input1) internal returns (euint32) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint32(0);
        }

        return euint32.wrap(Impl.square(Utils.EUINT32_TFHE, euint32.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 64-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 64 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint64 containing the square of the input
    function square(euint64 input1) internal returns (euint64) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint64(0);
        }

        return euint64.wrap(Impl.square(Utils.EUINT64_TFHE, euint64.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 128-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 128 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint128 containing the square of the input
    function square(euint128 input1) internal returns (euint128) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint128(0);
        }

        return euint128.wrap(Impl.square(Utils.EUINT128_TFHE, euint128.unwrap(input1)));
    }

    /// @notice Performs the square operation on an encrypted 256-bit unsigned integer
    /// @dev Verifies that the input is initialized, defaulting to 0 if not.
    ///      Note: The result may overflow if input * input exceeds 256 bits.
    /// @param input1 The input ciphertext to square
    /// @return An euint256 containing the square of the input
    function square(euint256 input1) internal returns (euint256) {
        if (!Common.isInitialized(input1)) {
            input1 = asEuint256(0);
        }

        return euint256.wrap(Impl.square(Utils.EUINT256_TFHE, euint256.unwrap(input1)));
    }
    /// @notice Generates a random value of a euint8 type for provided securityZone
    /// @dev Generates a cryptographically secure random 8-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 8-bit unsigned integer (euint8)
    function randomEuint8(int32 securityZone) internal returns (euint8) {
        return euint8.wrap(Impl.random(Utils.EUINT8_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint8 type
    /// @dev Generates a cryptographically secure random 8-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 8-bit unsigned integer (euint8)
    function randomEuint8() internal returns (euint8) {
        return randomEuint8(0);
    }
    /// @notice Generates a random value of a euint16 type for provided securityZone
    /// @dev Generates a cryptographically secure random 16-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 16-bit unsigned integer (euint16)
    function randomEuint16(int32 securityZone) internal returns (euint16) {
        return euint16.wrap(Impl.random(Utils.EUINT16_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint16 type
    /// @dev Generates a cryptographically secure random 16-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 16-bit unsigned integer (euint16)
    function randomEuint16() internal returns (euint16) {
        return randomEuint16(0);
    }
    /// @notice Generates a random value of a euint32 type for provided securityZone
    /// @dev Generates a cryptographically secure random 32-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 32-bit unsigned integer (euint32)
    function randomEuint32(int32 securityZone) internal returns (euint32) {
        return euint32.wrap(Impl.random(Utils.EUINT32_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint32 type
    /// @dev Generates a cryptographically secure random 32-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 32-bit unsigned integer (euint32)
    function randomEuint32() internal returns (euint32) {
        return randomEuint32(0);
    }
    /// @notice Generates a random value of a euint64 type for provided securityZone
    /// @dev Generates a cryptographically secure random 64-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 64-bit unsigned integer (euint64)
    function randomEuint64(int32 securityZone) internal returns (euint64) {
        return euint64.wrap(Impl.random(Utils.EUINT64_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint64 type
    /// @dev Generates a cryptographically secure random 64-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 64-bit unsigned integer (euint64)
    function randomEuint64() internal returns (euint64) {
        return randomEuint64(0);
    }
    /// @notice Generates a random value of a euint128 type for provided securityZone
    /// @dev Generates a cryptographically secure random 128-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 128-bit unsigned integer (euint128)
    function randomEuint128(int32 securityZone) internal returns (euint128) {
        return euint128.wrap(Impl.random(Utils.EUINT128_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint128 type
    /// @dev Generates a cryptographically secure random 128-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 128-bit unsigned integer (euint128)
    function randomEuint128() internal returns (euint128) {
        return randomEuint128(0);
    }
    /// @notice Generates a random value of a euint256 type for provided securityZone
    /// @dev Generates a cryptographically secure random 256-bit unsigned integer in encrypted form.
    ///      The generated value is fully encrypted and cannot be predicted by any party.
    /// @param securityZone The security zone identifier to use for random value generation.
    /// @return A randomly generated encrypted 256-bit unsigned integer (euint256)
    function randomEuint256(int32 securityZone) internal returns (euint256) {
        return euint256.wrap(Impl.random(Utils.EUINT256_TFHE, 0, securityZone));
    }
    /// @notice Generates a random value of a euint256 type
    /// @dev Generates a cryptographically secure random 256-bit unsigned integer in encrypted form
    ///      using the default security zone (0). The generated value is fully encrypted and
    ///      cannot be predicted by any party.
    /// @return A randomly generated encrypted 256-bit unsigned integer (euint256)
    function randomEuint256() internal returns (euint256) {
        return randomEuint256(0);
    }

    /// @notice Verifies and converts an inEbool input to an ebool encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An ebool containing the verified encrypted value
    function asEbool(InEbool memory value) internal returns (ebool) {
        uint8 expectedUtype = Utils.EBOOL_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }

        return ebool.wrap(Impl.verifyInput(Utils.inputFromEbool(value)));
    }

    /// @notice Verifies and converts an InEuint8 input to an euint8 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint8 containing the verified encrypted value
    function asEuint8(InEuint8 memory value) internal returns (euint8) {
        uint8 expectedUtype = Utils.EUINT8_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint8.wrap(Impl.verifyInput(Utils.inputFromEuint8(value)));
    }

    /// @notice Verifies and converts an InEuint16 input to an euint16 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint16 containing the verified encrypted value
    function asEuint16(InEuint16 memory value) internal returns (euint16) {
        uint8 expectedUtype = Utils.EUINT16_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint16.wrap(Impl.verifyInput(Utils.inputFromEuint16(value)));
    }

    /// @notice Verifies and converts an InEuint32 input to an euint32 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint32 containing the verified encrypted value
    function asEuint32(InEuint32 memory value) internal returns (euint32) {
        uint8 expectedUtype = Utils.EUINT32_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint32.wrap(Impl.verifyInput(Utils.inputFromEuint32(value)));
    }

    /// @notice Verifies and converts an InEuint64 input to an euint64 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint64 containing the verified encrypted value
    function asEuint64(InEuint64 memory value) internal returns (euint64) {
        uint8 expectedUtype = Utils.EUINT64_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint64.wrap(Impl.verifyInput(Utils.inputFromEuint64(value)));
    }

    /// @notice Verifies and converts an InEuint128 input to an euint128 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint128 containing the verified encrypted value
    function asEuint128(InEuint128 memory value) internal returns (euint128) {
        uint8 expectedUtype = Utils.EUINT128_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint128.wrap(Impl.verifyInput(Utils.inputFromEuint128(value)));
    }

    /// @notice Verifies and converts an InEuint256 input to an euint256 encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An euint256 containing the verified encrypted value
    function asEuint256(InEuint256 memory value) internal returns (euint256) {
        uint8 expectedUtype = Utils.EUINT256_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return euint256.wrap(Impl.verifyInput(Utils.inputFromEuint256(value)));
    }

    /// @notice Verifies and converts an InEaddress input to an eaddress encrypted type
    /// @dev Verifies the input signature and security parameters before converting to the encrypted type
    /// @param value The input value containing hash, type, security zone and signature
    /// @return An eaddress containing the verified encrypted value
    function asEaddress(InEaddress memory value) internal returns (eaddress) {
        uint8 expectedUtype = Utils.EADDRESS_TFHE;
        if (value.utype != expectedUtype) {
            revert InvalidEncryptedInput(value.utype, expectedUtype);
        }


        return eaddress.wrap(Impl.verifyInput(Utils.inputFromEaddress(value)));
    }

    // ********** TYPE CASTING ************* //
    /// @notice Converts a ebool to an euint8
    function asEuint8(ebool value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a ebool to an euint16
    function asEuint16(ebool value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a ebool to an euint32
    function asEuint32(ebool value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a ebool to an euint64
    function asEuint64(ebool value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a ebool to an euint128
    function asEuint128(ebool value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a ebool to an euint256
    function asEuint256(ebool value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(ebool.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint8 to an ebool
    function asEbool(euint8 value) internal returns (ebool) {
        return ne(value, asEuint8(0));
    }
    /// @notice Converts a euint8 to an euint16
    function asEuint16(euint8 value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(euint8.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a euint8 to an euint32
    function asEuint32(euint8 value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(euint8.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a euint8 to an euint64
    function asEuint64(euint8 value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(euint8.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a euint8 to an euint128
    function asEuint128(euint8 value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(euint8.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a euint8 to an euint256
    function asEuint256(euint8 value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(euint8.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint16 to an ebool
    function asEbool(euint16 value) internal returns (ebool) {
        return ne(value, asEuint16(0));
    }
    /// @notice Converts a euint16 to an euint8
    function asEuint8(euint16 value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(euint16.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a euint16 to an euint32
    function asEuint32(euint16 value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(euint16.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a euint16 to an euint64
    function asEuint64(euint16 value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(euint16.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a euint16 to an euint128
    function asEuint128(euint16 value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(euint16.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a euint16 to an euint256
    function asEuint256(euint16 value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(euint16.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint32 to an ebool
    function asEbool(euint32 value) internal returns (ebool) {
        return ne(value, asEuint32(0));
    }
    /// @notice Converts a euint32 to an euint8
    function asEuint8(euint32 value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(euint32.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a euint32 to an euint16
    function asEuint16(euint32 value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(euint32.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a euint32 to an euint64
    function asEuint64(euint32 value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(euint32.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a euint32 to an euint128
    function asEuint128(euint32 value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(euint32.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a euint32 to an euint256
    function asEuint256(euint32 value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(euint32.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint64 to an ebool
    function asEbool(euint64 value) internal returns (ebool) {
        return ne(value, asEuint64(0));
    }
    /// @notice Converts a euint64 to an euint8
    function asEuint8(euint64 value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(euint64.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a euint64 to an euint16
    function asEuint16(euint64 value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(euint64.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a euint64 to an euint32
    function asEuint32(euint64 value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(euint64.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a euint64 to an euint128
    function asEuint128(euint64 value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(euint64.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a euint64 to an euint256
    function asEuint256(euint64 value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(euint64.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint128 to an ebool
    function asEbool(euint128 value) internal returns (ebool) {
        return ne(value, asEuint128(0));
    }
    /// @notice Converts a euint128 to an euint8
    function asEuint8(euint128 value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(euint128.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a euint128 to an euint16
    function asEuint16(euint128 value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(euint128.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a euint128 to an euint32
    function asEuint32(euint128 value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(euint128.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a euint128 to an euint64
    function asEuint64(euint128 value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(euint128.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a euint128 to an euint256
    function asEuint256(euint128 value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(euint128.unwrap(value), Utils.EUINT256_TFHE));
    }

    /// @notice Converts a euint256 to an ebool
    function asEbool(euint256 value) internal returns (ebool) {
        return ne(value, asEuint256(0));
    }
    /// @notice Converts a euint256 to an euint8
    function asEuint8(euint256 value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(euint256.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a euint256 to an euint16
    function asEuint16(euint256 value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(euint256.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a euint256 to an euint32
    function asEuint32(euint256 value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(euint256.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a euint256 to an euint64
    function asEuint64(euint256 value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(euint256.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a euint256 to an euint128
    function asEuint128(euint256 value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(euint256.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a euint256 to an eaddress
    function asEaddress(euint256 value) internal returns (eaddress) {
        return eaddress.wrap(Impl.cast(euint256.unwrap(value), Utils.EADDRESS_TFHE));
    }

    /// @notice Converts a eaddress to an ebool
    function asEbool(eaddress value) internal returns (ebool) {
        return ne(value, asEaddress(address(0)));
    }
    /// @notice Converts a eaddress to an euint8
    function asEuint8(eaddress value) internal returns (euint8) {
        return euint8.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT8_TFHE));
    }
    /// @notice Converts a eaddress to an euint16
    function asEuint16(eaddress value) internal returns (euint16) {
        return euint16.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT16_TFHE));
    }
    /// @notice Converts a eaddress to an euint32
    function asEuint32(eaddress value) internal returns (euint32) {
        return euint32.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT32_TFHE));
    }
    /// @notice Converts a eaddress to an euint64
    function asEuint64(eaddress value) internal returns (euint64) {
        return euint64.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT64_TFHE));
    }
    /// @notice Converts a eaddress to an euint128
    function asEuint128(eaddress value) internal returns (euint128) {
        return euint128.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT128_TFHE));
    }
    /// @notice Converts a eaddress to an euint256
    function asEuint256(eaddress value) internal returns (euint256) {
        return euint256.wrap(Impl.cast(eaddress.unwrap(value), Utils.EUINT256_TFHE));
    }
    /// @notice Converts a plaintext boolean value to a ciphertext ebool
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    /// @return A ciphertext representation of the input
    function asEbool(bool value) internal returns (ebool) {
        return asEbool(value, 0);
    }
    /// @notice Converts a plaintext boolean value to a ciphertext ebool, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    /// @return A ciphertext representation of the input
    function asEbool(bool value, int32 securityZone) internal returns (ebool) {
        uint256 sVal = 0;
        if (value) {
            sVal = 1;
        }
        uint256 ct = Impl.trivialEncrypt(sVal, Utils.EBOOL_TFHE, securityZone);
        return ebool.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint8
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint8(uint256 value) internal returns (euint8) {
        return asEuint8(value, 0);
    }
    /// @notice Converts a uint256 to an euint8, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint8(uint256 value, int32 securityZone) internal returns (euint8) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT8_TFHE, securityZone);
        return euint8.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint16
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint16(uint256 value) internal returns (euint16) {
        return asEuint16(value, 0);
    }
    /// @notice Converts a uint256 to an euint16, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint16(uint256 value, int32 securityZone) internal returns (euint16) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT16_TFHE, securityZone);
        return euint16.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint32
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint32(uint256 value) internal returns (euint32) {
        return asEuint32(value, 0);
    }
    /// @notice Converts a uint256 to an euint32, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint32(uint256 value, int32 securityZone) internal returns (euint32) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT32_TFHE, securityZone);
        return euint32.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint64
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint64(uint256 value) internal returns (euint64) {
        return asEuint64(value, 0);
    }
    /// @notice Converts a uint256 to an euint64, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint64(uint256 value, int32 securityZone) internal returns (euint64) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT64_TFHE, securityZone);
        return euint64.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint128
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint128(uint256 value) internal returns (euint128) {
        return asEuint128(value, 0);
    }
    /// @notice Converts a uint256 to an euint128, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint128(uint256 value, int32 securityZone) internal returns (euint128) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT128_TFHE, securityZone);
        return euint128.wrap(ct);
    }
    /// @notice Converts a uint256 to an euint256
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint256(uint256 value) internal returns (euint256) {
        return asEuint256(value, 0);
    }
    /// @notice Converts a uint256 to an euint256, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    function asEuint256(uint256 value, int32 securityZone) internal returns (euint256) {
        uint256 ct = Impl.trivialEncrypt(value, Utils.EUINT256_TFHE, securityZone);
        return euint256.wrap(ct);
    }
    /// @notice Converts a address to an eaddress
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    /// Allows for a better user experience when working with eaddresses
    function asEaddress(address value) internal returns (eaddress) {
        return asEaddress(value, 0);
    }
    /// @notice Converts a address to an eaddress, specifying security zone
    /// @dev Privacy: The input value is public, therefore the resulting ciphertext should be considered public until involved in an fhe operation
    /// Allows for a better user experience when working with eaddresses
    function asEaddress(address value, int32 securityZone) internal returns (eaddress) {
        uint256 ct = Impl.trivialEncrypt(uint256(uint160(value)), Utils.EADDRESS_TFHE, securityZone);
        return eaddress.wrap(ct);
    }

    /// @notice Grants permission to an account to operate on the encrypted boolean value
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted boolean value to grant access to
    /// @param account The address being granted permission
    function allow(ebool ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(ebool.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 8-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint8 value to grant access to
    /// @param account The address being granted permission
    function allow(euint8 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint8.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 16-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint16 value to grant access to
    /// @param account The address being granted permission
    function allow(euint16 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint16.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 32-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint32 value to grant access to
    /// @param account The address being granted permission
    function allow(euint32 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint32.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 64-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint64 value to grant access to
    /// @param account The address being granted permission
    function allow(euint64 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint64.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 128-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint128 value to grant access to
    /// @param account The address being granted permission
    function allow(euint128 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint128.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted 256-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted uint256 value to grant access to
    /// @param account The address being granted permission
    function allow(euint256 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint256.unwrap(ctHash), account);
    }

    /// @notice Grants permission to an account to operate on the encrypted address
    /// @dev Allows the specified account to access the ciphertext
    /// @param ctHash The encrypted address value to grant access to
    /// @param account The address being granted permission
    function allow(eaddress ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(eaddress.unwrap(ctHash), account);
    }

    /// @notice Grants global permission to operate on the encrypted boolean value
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted boolean value to grant global access to
    function allowGlobal(ebool ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(ebool.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 8-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint8 value to grant global access to
    function allowGlobal(euint8 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint8.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 16-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint16 value to grant global access to
    function allowGlobal(euint16 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint16.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 32-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint32 value to grant global access to
    function allowGlobal(euint32 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint32.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 64-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint64 value to grant global access to
    function allowGlobal(euint64 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint64.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 128-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint128 value to grant global access to
    function allowGlobal(euint128 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint128.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted 256-bit unsigned integer
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted uint256 value to grant global access to
    function allowGlobal(euint256 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(euint256.unwrap(ctHash));
    }

    /// @notice Grants global permission to operate on the encrypted address
    /// @dev Allows all accounts to access the ciphertext
    /// @param ctHash The encrypted address value to grant global access to
    function allowGlobal(eaddress ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowGlobal(eaddress.unwrap(ctHash));
    }

    /// @notice Checks if an account has permission to operate on the encrypted boolean value
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted boolean value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(ebool ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(ebool.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 8-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint8 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint8 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint8.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 16-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint16 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint16 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint16.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 32-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint32 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint32 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint32.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 64-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint64 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint64 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint64.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 128-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint128 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint128 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint128.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted 256-bit unsigned integer
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted uint256 value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(euint256 ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(euint256.unwrap(ctHash), account);
    }

    /// @notice Checks if an account has permission to operate on the encrypted address
    /// @dev Returns whether the specified account can access the ciphertext
    /// @param ctHash The encrypted address value to check access for
    /// @param account The address to check permissions for
    /// @return True if the account has permission, false otherwise
    function isAllowed(eaddress ctHash, address account) internal returns (bool) {
        return ITaskManager(TASK_MANAGER_ADDRESS).isAllowed(eaddress.unwrap(ctHash), account);
    }

    /// @notice Grants permission to the current contract to operate on the encrypted boolean value
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted boolean value to grant access to
    function allowThis(ebool ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(ebool.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 8-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint8 value to grant access to
    function allowThis(euint8 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint8.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 16-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint16 value to grant access to
    function allowThis(euint16 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint16.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 32-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint32 value to grant access to
    function allowThis(euint32 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint32.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 64-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint64 value to grant access to
    function allowThis(euint64 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint64.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 128-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint128 value to grant access to
    function allowThis(euint128 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint128.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted 256-bit unsigned integer
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted uint256 value to grant access to
    function allowThis(euint256 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint256.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the current contract to operate on the encrypted address
    /// @dev Allows this contract to access the ciphertext
    /// @param ctHash The encrypted address value to grant access to
    function allowThis(eaddress ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(eaddress.unwrap(ctHash), address(this));
    }

    /// @notice Grants permission to the message sender to operate on the encrypted boolean value
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted boolean value to grant access to
    function allowSender(ebool ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(ebool.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 8-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint8 value to grant access to
    function allowSender(euint8 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint8.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 16-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint16 value to grant access to
    function allowSender(euint16 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint16.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 32-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint32 value to grant access to
    function allowSender(euint32 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint32.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 64-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint64 value to grant access to
    function allowSender(euint64 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint64.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 128-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint128 value to grant access to
    function allowSender(euint128 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint128.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted 256-bit unsigned integer
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted uint256 value to grant access to
    function allowSender(euint256 ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(euint256.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants permission to the message sender to operate on the encrypted address
    /// @dev Allows the transaction sender to access the ciphertext
    /// @param ctHash The encrypted address value to grant access to
    function allowSender(eaddress ctHash) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allow(eaddress.unwrap(ctHash), msg.sender);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted boolean value
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted boolean value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(ebool ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(ebool.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 8-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint8 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint8 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint8.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 16-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint16 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint16 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint16.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 32-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint32 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint32 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint32.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 64-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint64 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint64 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint64.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 128-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint128 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint128 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint128.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted 256-bit unsigned integer
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted uint256 value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(euint256 ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(euint256.unwrap(ctHash), account);
    }

    /// @notice Grants temporary permission to an account to operate on the encrypted address
    /// @dev Allows the specified account to access the ciphertext for the current transaction only
    /// @param ctHash The encrypted address value to grant temporary access to
    /// @param account The address being granted temporary permission
    function allowTransient(eaddress ctHash, address account) internal {
        ITaskManager(TASK_MANAGER_ADDRESS).allowTransient(eaddress.unwrap(ctHash), account);
    }


}
// ********** BINDING DEFS ************* //

using BindingsEbool for ebool global;
library BindingsEbool {

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return the result of the eq
    function eq(ebool lhs, ebool rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return the result of the ne
    function ne(ebool lhs, ebool rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @return the result of the not
    function not(ebool lhs) internal returns (ebool) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return the result of the and
    function and(ebool lhs, ebool rhs) internal returns (ebool) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return the result of the or
    function or(ebool lhs, ebool rhs) internal returns (ebool) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type ebool
    /// @param rhs second input of type ebool
    /// @return the result of the xor
    function xor(ebool lhs, ebool rhs) internal returns (ebool) {
        return FHE.xor(lhs, rhs);
    }
    function toU8(ebool value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(ebool value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(ebool value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(ebool value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(ebool value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(ebool value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(ebool value) internal {
        FHE.decrypt(value);
    }
    function allow(ebool ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(ebool ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(ebool ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(ebool ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(ebool ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(ebool ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint8 for euint8 global;
library BindingsEuint8 {

    /// @notice Performs the add operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the add
    function add(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.add(lhs, rhs);
    }

    /// @notice Performs the mul operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the mul
    function mul(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.mul(lhs, rhs);
    }

    /// @notice Performs the div operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the div
    function div(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.div(lhs, rhs);
    }

    /// @notice Performs the sub operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the sub
    function sub(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.sub(lhs, rhs);
    }

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the eq
    function eq(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the ne
    function ne(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @return the result of the not
    function not(euint8 lhs) internal returns (euint8) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the and
    function and(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the or
    function or(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the xor
    function xor(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.xor(lhs, rhs);
    }

    /// @notice Performs the gt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the gt
    function gt(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.gt(lhs, rhs);
    }

    /// @notice Performs the gte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the gte
    function gte(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.gte(lhs, rhs);
    }

    /// @notice Performs the lt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the lt
    function lt(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.lt(lhs, rhs);
    }

    /// @notice Performs the lte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the lte
    function lte(euint8 lhs, euint8 rhs) internal returns (ebool) {
        return FHE.lte(lhs, rhs);
    }

    /// @notice Performs the rem operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the rem
    function rem(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.rem(lhs, rhs);
    }

    /// @notice Performs the max operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the max
    function max(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.max(lhs, rhs);
    }

    /// @notice Performs the min operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the min
    function min(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.min(lhs, rhs);
    }

    /// @notice Performs the shl operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the shl
    function shl(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.shl(lhs, rhs);
    }

    /// @notice Performs the shr operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the shr
    function shr(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.shr(lhs, rhs);
    }

    /// @notice Performs the rol operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the rol
    function rol(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.rol(lhs, rhs);
    }

    /// @notice Performs the ror operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @param rhs second input of type euint8
    /// @return the result of the ror
    function ror(euint8 lhs, euint8 rhs) internal returns (euint8) {
        return FHE.ror(lhs, rhs);
    }

    /// @notice Performs the square operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint8
    /// @return the result of the square
    function square(euint8 lhs) internal returns (euint8) {
        return FHE.square(lhs);
    }
    function toBool(euint8 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU16(euint8 value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(euint8 value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(euint8 value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(euint8 value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(euint8 value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(euint8 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint8 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint8 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint8 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint8 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint8 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint8 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint16 for euint16 global;
library BindingsEuint16 {

    /// @notice Performs the add operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the add
    function add(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.add(lhs, rhs);
    }

    /// @notice Performs the mul operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the mul
    function mul(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.mul(lhs, rhs);
    }

    /// @notice Performs the div operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the div
    function div(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.div(lhs, rhs);
    }

    /// @notice Performs the sub operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the sub
    function sub(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.sub(lhs, rhs);
    }

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the eq
    function eq(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the ne
    function ne(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @return the result of the not
    function not(euint16 lhs) internal returns (euint16) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the and
    function and(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the or
    function or(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the xor
    function xor(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.xor(lhs, rhs);
    }

    /// @notice Performs the gt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the gt
    function gt(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.gt(lhs, rhs);
    }

    /// @notice Performs the gte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the gte
    function gte(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.gte(lhs, rhs);
    }

    /// @notice Performs the lt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the lt
    function lt(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.lt(lhs, rhs);
    }

    /// @notice Performs the lte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the lte
    function lte(euint16 lhs, euint16 rhs) internal returns (ebool) {
        return FHE.lte(lhs, rhs);
    }

    /// @notice Performs the rem operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the rem
    function rem(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.rem(lhs, rhs);
    }

    /// @notice Performs the max operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the max
    function max(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.max(lhs, rhs);
    }

    /// @notice Performs the min operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the min
    function min(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.min(lhs, rhs);
    }

    /// @notice Performs the shl operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the shl
    function shl(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.shl(lhs, rhs);
    }

    /// @notice Performs the shr operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the shr
    function shr(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.shr(lhs, rhs);
    }

    /// @notice Performs the rol operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the rol
    function rol(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.rol(lhs, rhs);
    }

    /// @notice Performs the ror operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @param rhs second input of type euint16
    /// @return the result of the ror
    function ror(euint16 lhs, euint16 rhs) internal returns (euint16) {
        return FHE.ror(lhs, rhs);
    }

    /// @notice Performs the square operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint16
    /// @return the result of the square
    function square(euint16 lhs) internal returns (euint16) {
        return FHE.square(lhs);
    }
    function toBool(euint16 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(euint16 value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU32(euint16 value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(euint16 value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(euint16 value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(euint16 value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(euint16 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint16 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint16 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint16 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint16 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint16 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint16 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint32 for euint32 global;
library BindingsEuint32 {

    /// @notice Performs the add operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the add
    function add(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.add(lhs, rhs);
    }

    /// @notice Performs the mul operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the mul
    function mul(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.mul(lhs, rhs);
    }

    /// @notice Performs the div operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the div
    function div(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.div(lhs, rhs);
    }

    /// @notice Performs the sub operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the sub
    function sub(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.sub(lhs, rhs);
    }

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the eq
    function eq(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the ne
    function ne(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @return the result of the not
    function not(euint32 lhs) internal returns (euint32) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the and
    function and(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the or
    function or(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the xor
    function xor(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.xor(lhs, rhs);
    }

    /// @notice Performs the gt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the gt
    function gt(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.gt(lhs, rhs);
    }

    /// @notice Performs the gte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the gte
    function gte(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.gte(lhs, rhs);
    }

    /// @notice Performs the lt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the lt
    function lt(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.lt(lhs, rhs);
    }

    /// @notice Performs the lte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the lte
    function lte(euint32 lhs, euint32 rhs) internal returns (ebool) {
        return FHE.lte(lhs, rhs);
    }

    /// @notice Performs the rem operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the rem
    function rem(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.rem(lhs, rhs);
    }

    /// @notice Performs the max operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the max
    function max(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.max(lhs, rhs);
    }

    /// @notice Performs the min operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the min
    function min(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.min(lhs, rhs);
    }

    /// @notice Performs the shl operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the shl
    function shl(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.shl(lhs, rhs);
    }

    /// @notice Performs the shr operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the shr
    function shr(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.shr(lhs, rhs);
    }

    /// @notice Performs the rol operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the rol
    function rol(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.rol(lhs, rhs);
    }

    /// @notice Performs the ror operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @param rhs second input of type euint32
    /// @return the result of the ror
    function ror(euint32 lhs, euint32 rhs) internal returns (euint32) {
        return FHE.ror(lhs, rhs);
    }

    /// @notice Performs the square operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint32
    /// @return the result of the square
    function square(euint32 lhs) internal returns (euint32) {
        return FHE.square(lhs);
    }
    function toBool(euint32 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(euint32 value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(euint32 value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU64(euint32 value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(euint32 value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(euint32 value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(euint32 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint32 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint32 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint32 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint32 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint32 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint32 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint64 for euint64 global;
library BindingsEuint64 {

    /// @notice Performs the add operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the add
    function add(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.add(lhs, rhs);
    }

    /// @notice Performs the mul operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the mul
    function mul(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.mul(lhs, rhs);
    }

    /// @notice Performs the sub operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the sub
    function sub(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.sub(lhs, rhs);
    }

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the eq
    function eq(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the ne
    function ne(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @return the result of the not
    function not(euint64 lhs) internal returns (euint64) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the and
    function and(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the or
    function or(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the xor
    function xor(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.xor(lhs, rhs);
    }

    /// @notice Performs the gt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the gt
    function gt(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.gt(lhs, rhs);
    }

    /// @notice Performs the gte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the gte
    function gte(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.gte(lhs, rhs);
    }

    /// @notice Performs the lt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the lt
    function lt(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.lt(lhs, rhs);
    }

    /// @notice Performs the lte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the lte
    function lte(euint64 lhs, euint64 rhs) internal returns (ebool) {
        return FHE.lte(lhs, rhs);
    }

    /// @notice Performs the max operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the max
    function max(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.max(lhs, rhs);
    }

    /// @notice Performs the min operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the min
    function min(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.min(lhs, rhs);
    }

    /// @notice Performs the shl operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the shl
    function shl(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.shl(lhs, rhs);
    }

    /// @notice Performs the shr operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the shr
    function shr(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.shr(lhs, rhs);
    }

    /// @notice Performs the rol operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the rol
    function rol(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.rol(lhs, rhs);
    }

    /// @notice Performs the ror operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @param rhs second input of type euint64
    /// @return the result of the ror
    function ror(euint64 lhs, euint64 rhs) internal returns (euint64) {
        return FHE.ror(lhs, rhs);
    }

    /// @notice Performs the square operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint64
    /// @return the result of the square
    function square(euint64 lhs) internal returns (euint64) {
        return FHE.square(lhs);
    }
    function toBool(euint64 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(euint64 value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(euint64 value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(euint64 value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU128(euint64 value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(euint64 value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(euint64 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint64 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint64 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint64 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint64 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint64 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint64 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint128 for euint128 global;
library BindingsEuint128 {

    /// @notice Performs the add operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the add
    function add(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.add(lhs, rhs);
    }

    /// @notice Performs the sub operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the sub
    function sub(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.sub(lhs, rhs);
    }

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the eq
    function eq(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the ne
    function ne(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }

    /// @notice Performs the not operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @return the result of the not
    function not(euint128 lhs) internal returns (euint128) {
        return FHE.not(lhs);
    }

    /// @notice Performs the and operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the and
    function and(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.and(lhs, rhs);
    }

    /// @notice Performs the or operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the or
    function or(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.or(lhs, rhs);
    }

    /// @notice Performs the xor operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the xor
    function xor(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.xor(lhs, rhs);
    }

    /// @notice Performs the gt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the gt
    function gt(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.gt(lhs, rhs);
    }

    /// @notice Performs the gte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the gte
    function gte(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.gte(lhs, rhs);
    }

    /// @notice Performs the lt operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the lt
    function lt(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.lt(lhs, rhs);
    }

    /// @notice Performs the lte operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the lte
    function lte(euint128 lhs, euint128 rhs) internal returns (ebool) {
        return FHE.lte(lhs, rhs);
    }

    /// @notice Performs the max operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the max
    function max(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.max(lhs, rhs);
    }

    /// @notice Performs the min operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the min
    function min(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.min(lhs, rhs);
    }

    /// @notice Performs the shl operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the shl
    function shl(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.shl(lhs, rhs);
    }

    /// @notice Performs the shr operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the shr
    function shr(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.shr(lhs, rhs);
    }

    /// @notice Performs the rol operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the rol
    function rol(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.rol(lhs, rhs);
    }

    /// @notice Performs the ror operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint128
    /// @param rhs second input of type euint128
    /// @return the result of the ror
    function ror(euint128 lhs, euint128 rhs) internal returns (euint128) {
        return FHE.ror(lhs, rhs);
    }
    function toBool(euint128 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(euint128 value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(euint128 value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(euint128 value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(euint128 value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU256(euint128 value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(euint128 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint128 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint128 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint128 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint128 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint128 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint128 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEuint256 for euint256 global;
library BindingsEuint256 {

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return the result of the eq
    function eq(euint256 lhs, euint256 rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type euint256
    /// @param rhs second input of type euint256
    /// @return the result of the ne
    function ne(euint256 lhs, euint256 rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }
    function toBool(euint256 value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(euint256 value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(euint256 value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(euint256 value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(euint256 value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(euint256 value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toEaddress(euint256 value) internal returns (eaddress) {
        return FHE.asEaddress(value);
    }
    function decrypt(euint256 value) internal {
        FHE.decrypt(value);
    }
    function allow(euint256 ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(euint256 ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(euint256 ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(euint256 ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(euint256 ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(euint256 ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

using BindingsEaddress for eaddress global;
library BindingsEaddress {

    /// @notice Performs the eq operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type eaddress
    /// @param rhs second input of type eaddress
    /// @return the result of the eq
    function eq(eaddress lhs, eaddress rhs) internal returns (ebool) {
        return FHE.eq(lhs, rhs);
    }

    /// @notice Performs the ne operation
    /// @dev Pure in this function is marked as a hack/workaround - note that this function is NOT pure as fetches of ciphertexts require state access
    /// @param lhs input of type eaddress
    /// @param rhs second input of type eaddress
    /// @return the result of the ne
    function ne(eaddress lhs, eaddress rhs) internal returns (ebool) {
        return FHE.ne(lhs, rhs);
    }
    function toBool(eaddress value) internal  returns (ebool) {
        return FHE.asEbool(value);
    }
    function toU8(eaddress value) internal returns (euint8) {
        return FHE.asEuint8(value);
    }
    function toU16(eaddress value) internal returns (euint16) {
        return FHE.asEuint16(value);
    }
    function toU32(eaddress value) internal returns (euint32) {
        return FHE.asEuint32(value);
    }
    function toU64(eaddress value) internal returns (euint64) {
        return FHE.asEuint64(value);
    }
    function toU128(eaddress value) internal returns (euint128) {
        return FHE.asEuint128(value);
    }
    function toU256(eaddress value) internal returns (euint256) {
        return FHE.asEuint256(value);
    }
    function decrypt(eaddress value) internal {
        FHE.decrypt(value);
    }
    function allow(eaddress ctHash, address account) internal {
        FHE.allow(ctHash, account);
    }
    function isAllowed(eaddress ctHash, address account) internal returns (bool) {
        return FHE.isAllowed(ctHash, account);
    }
    function allowThis(eaddress ctHash) internal {
        FHE.allowThis(ctHash);
    }
    function allowGlobal(eaddress ctHash) internal {
        FHE.allowGlobal(ctHash);
    }
    function allowSender(eaddress ctHash) internal {
        FHE.allowSender(ctHash);
    }
    function allowTransient(eaddress ctHash, address account) internal {
        FHE.allowTransient(ctHash, account);
    }
}

// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.25 <0.9.0;

struct EncryptedInput {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEbool {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint8 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint16 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint32 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint64 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint128 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}

struct InEuint256 {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}
struct InEaddress {
    uint256 ctHash;
    uint8 securityZone;
    uint8 utype;
    bytes signature;
}


// Order is set as in fheos/precompiles/types/types.go
enum FunctionId {
    _0,             // 0 - GetNetworkKey
    _1,             // 1 - Verify
    cast,           // 2
    sealoutput,     // 3
    select,         // 4 - select
    _5,             // 5 - req
    decrypt,        // 6
    sub,            // 7
    add,            // 8
    xor,            // 9
    and,            // 10
    or,             // 11
    not,            // 12
    div,            // 13
    rem,            // 14
    mul,            // 15
    shl,            // 16
    shr,            // 17
    gte,            // 18
    lte,            // 19
    lt,             // 20
    gt,             // 21
    min,            // 22
    max,            // 23
    eq,             // 24
    ne,             // 25
    trivialEncrypt, // 26
    random,         // 27
    rol,            // 28
    ror,            // 29
    square,         // 30
    _31             // 31
}

interface ITaskManager {
    function createTask(uint8 returnType, FunctionId funcId, uint256[] memory encryptedInputs, uint256[] memory extraInputs) external returns (uint256);

    function createDecryptTask(uint256 ctHash, address requestor) external;
    function verifyInput(EncryptedInput memory input, address sender) external returns (uint256);

    function allow(uint256 ctHash, address account) external;
    function isAllowed(uint256 ctHash, address account) external returns (bool);
    function allowGlobal(uint256 ctHash) external;
    function allowTransient(uint256 ctHash, address account) external;
    function getDecryptResultSafe(uint256 ctHash) external view returns (uint256, bool);
    function getDecryptResult(uint256 ctHash) external view returns (uint256);
}

library Utils {
    // Values used to communicate types to the runtime.
    // Must match values defined in warp-drive protobufs for everything to
    uint8 internal constant EUINT8_TFHE = 2;
    uint8 internal constant EUINT16_TFHE = 3;
    uint8 internal constant EUINT32_TFHE = 4;
    uint8 internal constant EUINT64_TFHE = 5;
    uint8 internal constant EUINT128_TFHE = 6;
    uint8 internal constant EUINT256_TFHE = 8;
    uint8 internal constant EADDRESS_TFHE = 7;
    uint8 internal constant EBOOL_TFHE = 0;

    function functionIdToString(FunctionId _functionId) internal pure returns (string memory) {
        if (_functionId == FunctionId.cast) return "cast";
        if (_functionId == FunctionId.sealoutput) return "sealOutput";
        if (_functionId == FunctionId.select) return "select";
        if (_functionId == FunctionId.decrypt) return "decrypt";
        if (_functionId == FunctionId.sub) return "sub";
        if (_functionId == FunctionId.add) return "add";
        if (_functionId == FunctionId.xor) return "xor";
        if (_functionId == FunctionId.and) return "and";
        if (_functionId == FunctionId.or) return "or";
        if (_functionId == FunctionId.not) return "not";
        if (_functionId == FunctionId.div) return "div";
        if (_functionId == FunctionId.rem) return "rem";
        if (_functionId == FunctionId.mul) return "mul";
        if (_functionId == FunctionId.shl) return "shl";
        if (_functionId == FunctionId.shr) return "shr";
        if (_functionId == FunctionId.gte) return "gte";
        if (_functionId == FunctionId.lte) return "lte";
        if (_functionId == FunctionId.lt) return "lt";
        if (_functionId == FunctionId.gt) return "gt";
        if (_functionId == FunctionId.min) return "min";
        if (_functionId == FunctionId.max) return "max";
        if (_functionId == FunctionId.eq) return "eq";
        if (_functionId == FunctionId.ne) return "ne";
        if (_functionId == FunctionId.trivialEncrypt) return "trivialEncrypt";
        if (_functionId == FunctionId.random) return "random";
        if (_functionId == FunctionId.rol) return "rol";
        if (_functionId == FunctionId.ror) return "ror";
        if (_functionId == FunctionId.square) return "square";

        return "";
    }

    function inputFromEbool(InEbool memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EBOOL_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint8(InEuint8 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT8_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint16(InEuint16 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT16_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint32(InEuint32 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT32_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint64(InEuint64 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT64_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint128(InEuint128 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT128_TFHE,
            signature: input.signature
        });
    }

    function inputFromEuint256(InEuint256 memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EUINT256_TFHE,
            signature: input.signature
        });
    }

    function inputFromEaddress(InEaddress memory input) internal pure returns (EncryptedInput memory) {
        return EncryptedInput({
            ctHash: input.ctHash,
            securityZone: input.securityZone,
            utype: EADDRESS_TFHE,
            signature: input.signature
        });
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)

pragma solidity ^0.8.20;

import {Context} from "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * The initial owner is set to the address provided by the deployer. This can
 * later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    constructor(address initialOwner) {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC20InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC20InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     * @param allowance Amount of tokens a `spender` is allowed to operate with.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientAllowance(address spender, uint256 allowance, uint256 needed);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC20InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `spender` to be approved. Used in approvals.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC20InvalidSpender(address spender);
}

/**
 * @dev Standard ERC-721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in ERC-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

    /**
     * @dev Indicates a `tokenId` whose `owner` is the zero address.
     * @param tokenId Identifier number of a token.
     */
    error ERC721NonexistentToken(uint256 tokenId);

    /**
     * @dev Indicates an error related to the ownership over a particular token. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param tokenId Identifier number of a token.
     * @param owner Address of the current owner of a token.
     */
    error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC721InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC721InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param tokenId Identifier number of a token.
     */
    error ERC721InsufficientApproval(address operator, uint256 tokenId);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC721InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC721InvalidOperator(address operator);
}

/**
 * @dev Standard ERC-1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC1155InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC1155InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param owner Address of the current owner of a token.
     */
    error ERC1155MissingApprovalForAll(address operator, address owner);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC1155InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC1155InvalidOperator(address operator);

    /**
     * @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
     * Used in batch transfers.
     * @param idsLength Length of the array of token identifiers
     * @param valuesLength Length of the array of token amounts
     */
    error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/IERC1363.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";
import {IERC165} from "./IERC165.sol";

/**
 * @title IERC1363
 * @dev Interface of the ERC-1363 standard as defined in the https://eips.ethereum.org/EIPS/eip-1363[ERC-1363].
 *
 * Defines an extension interface for ERC-20 tokens that supports executing code on a recipient contract
 * after `transfer` or `transferFrom`, or code on a spender contract after `approve`, in a single transaction.
 */
interface IERC1363 is IERC20, IERC165 {
    /*
     * Note: the ERC-165 identifier for this interface is 0xb0202a11.
     * 0xb0202a11 ===
     *   bytes4(keccak256('transferAndCall(address,uint256)')) ^
     *   bytes4(keccak256('transferAndCall(address,uint256,bytes)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256,bytes)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256,bytes)'))
     */

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @param data Additional data with no specified format, sent in call to `spender`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value, bytes calldata data) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC165.sol)

pragma solidity ^0.8.20;

import {IERC165} from "../utils/introspection/IERC165.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../token/ERC20/IERC20.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC5267.sol)

pragma solidity ^0.8.20;

interface IERC5267 {
    /**
     * @dev MAY be emitted to signal that the domain could have changed.
     */
    event EIP712DomainChanged();

    /**
     * @dev returns the fields and values that describe the domain separator used by this contract for EIP-712
     * signature.
     */
    function eip712Domain()
        external
        view
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        );
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";
import {IERC20Metadata} from "./extensions/IERC20Metadata.sol";
import {Context} from "../../utils/Context.sol";
import {IERC20Errors} from "../../interfaces/draft-IERC6093.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 */
abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors {
    mapping(address account => uint256) private _balances;

    mapping(address account => mapping(address spender => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * Both values are immutable: they can only be set once during construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     */
    function transfer(address to, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, value);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `value` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, value);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Skips emitting an {Approval} event indicating an allowance update. This is not
     * required by the ERC. See {xref-ERC20-_approve-address-address-uint256-bool-}[_approve].
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function transferFrom(address from, address to, uint256 value) public virtual returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, value);
        _transfer(from, to, value);
        return true;
    }

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _transfer(address from, address to, uint256 value) internal {
        if (from == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        if (to == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(from, to, value);
    }

    /**
     * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
     * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
     * this function.
     *
     * Emits a {Transfer} event.
     */
    function _update(address from, address to, uint256 value) internal virtual {
        if (from == address(0)) {
            // Overflow check required: The rest of the code assumes that totalSupply never overflows
            _totalSupply += value;
        } else {
            uint256 fromBalance = _balances[from];
            if (fromBalance < value) {
                revert ERC20InsufficientBalance(from, fromBalance, value);
            }
            unchecked {
                // Overflow not possible: value <= fromBalance <= totalSupply.
                _balances[from] = fromBalance - value;
            }
        }

        if (to == address(0)) {
            unchecked {
                // Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply.
                _totalSupply -= value;
            }
        } else {
            unchecked {
                // Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256.
                _balances[to] += value;
            }
        }

        emit Transfer(from, to, value);
    }

    /**
     * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
     * Relies on the `_update` mechanism
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _mint(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(address(0), account, value);
    }

    /**
     * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
     * Relies on the `_update` mechanism.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead
     */
    function _burn(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        _update(account, address(0), value);
    }

    /**
     * @dev Sets `value` as the allowance of `spender` over the `owner`'s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address owner, address spender, uint256 value) internal {
        _approve(owner, spender, value, true);
    }

    /**
     * @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event.
     *
     * By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by
     * `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any
     * `Approval` event during `transferFrom` operations.
     *
     * Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to
     * true using the following override:
     *
     * ```solidity
     * function _approve(address owner, address spender, uint256 value, bool) internal virtual override {
     *     super._approve(owner, spender, value, true);
     * }
     * ```
     *
     * Requirements are the same as {_approve}.
     */
    function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual {
        if (owner == address(0)) {
            revert ERC20InvalidApprover(address(0));
        }
        if (spender == address(0)) {
            revert ERC20InvalidSpender(address(0));
        }
        _allowances[owner][spender] = value;
        if (emitEvent) {
            emit Approval(owner, spender, value);
        }
    }

    /**
     * @dev Updates `owner`'s allowance for `spender` based on spent `value`.
     *
     * Does not update the allowance value in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Does not emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 value) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance < type(uint256).max) {
            if (currentAllowance < value) {
                revert ERC20InsufficientAllowance(spender, currentAllowance, value);
            }
            unchecked {
                _approve(owner, spender, currentAllowance - value, false);
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC-20 standard.
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-20 standard as defined in the ERC.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the value of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the value of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 value) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the
     * allowance mechanism. `value` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 value) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";
import {IERC1363} from "../../../interfaces/IERC1363.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC-20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    /**
     * @dev An operation with an ERC-20 token failed.
     */
    error SafeERC20FailedOperation(address token);

    /**
     * @dev Indicates a failed `decreaseAllowance` request.
     */
    error SafeERC20FailedDecreaseAllowance(address spender, uint256 currentAllowance, uint256 requestedDecrease);

    /**
     * @dev Transfer `value` amount of `token` from the calling contract to `to`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transfer, (to, value)));
    }

    /**
     * @dev Transfer `value` amount of `token` from `from` to `to`, spending the approval given by `from` to the
     * calling contract. If `token` returns no value, non-reverting calls are assumed to be successful.
     */
    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transferFrom, (from, to, value)));
    }

    /**
     * @dev Variant of {safeTransfer} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransfer(IERC20 token, address to, uint256 value) internal returns (bool) {
        return _callOptionalReturnBool(token, abi.encodeCall(token.transfer, (to, value)));
    }

    /**
     * @dev Variant of {safeTransferFrom} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransferFrom(IERC20 token, address from, address to, uint256 value) internal returns (bool) {
        return _callOptionalReturnBool(token, abi.encodeCall(token.transferFrom, (from, to, value)));
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        forceApprove(token, spender, oldAllowance + value);
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `requestedDecrease`. If `token` returns no
     * value, non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 requestedDecrease) internal {
        unchecked {
            uint256 currentAllowance = token.allowance(address(this), spender);
            if (currentAllowance < requestedDecrease) {
                revert SafeERC20FailedDecreaseAllowance(spender, currentAllowance, requestedDecrease);
            }
            forceApprove(token, spender, currentAllowance - requestedDecrease);
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Meant to be used with tokens that require the approval
     * to be set to zero before setting it to a non-zero value, such as USDT.
     *
     * NOTE: If the token implements ERC-7674, this function will not modify any temporary allowance. This function
     * only sets the "standard" allowance. Any temporary allowance will remain active, in addition to the value being
     * set here.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        bytes memory approvalCall = abi.encodeCall(token.approve, (spender, value));

        if (!_callOptionalReturnBool(token, approvalCall)) {
            _callOptionalReturn(token, abi.encodeCall(token.approve, (spender, 0)));
            _callOptionalReturn(token, approvalCall);
        }
    }

    /**
     * @dev Performs an {ERC1363} transferAndCall, with a fallback to the simple {ERC20} transfer if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            safeTransfer(token, to, value);
        } else if (!token.transferAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferFromAndCall, with a fallback to the simple {ERC20} transferFrom if the target
     * has no code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferFromAndCallRelaxed(
        IERC1363 token,
        address from,
        address to,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length == 0) {
            safeTransferFrom(token, from, to, value);
        } else if (!token.transferFromAndCall(from, to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} approveAndCall, with a fallback to the simple {ERC20} approve if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * NOTE: When the recipient address (`to`) has no code (i.e. is an EOA), this function behaves as {forceApprove}.
     * Opposedly, when the recipient address (`to`) has code, this function only attempts to call {ERC1363-approveAndCall}
     * once without retrying, and relies on the returned value to be true.
     *
     * Reverts if the returned value is other than `true`.
     */
    function approveAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            forceApprove(token, to, value);
        } else if (!token.approveAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturnBool} that reverts if call fails to meet the requirements.
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        uint256 returnSize;
        uint256 returnValue;
        assembly ("memory-safe") {
            let success := call(gas(), token, 0, add(data, 0x20), mload(data), 0, 0x20)
            // bubble errors
            if iszero(success) {
                let ptr := mload(0x40)
                returndatacopy(ptr, 0, returndatasize())
                revert(ptr, returndatasize())
            }
            returnSize := returndatasize()
            returnValue := mload(0)
        }

        if (returnSize == 0 ? address(token).code.length == 0 : returnValue != 1) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturn} that silently catches all reverts and returns a bool instead.
     */
    function _callOptionalReturnBool(IERC20 token, bytes memory data) private returns (bool) {
        bool success;
        uint256 returnSize;
        uint256 returnValue;
        assembly ("memory-safe") {
            success := call(gas(), token, 0, add(data, 0x20), mload(data), 0, 0x20)
            returnSize := returndatasize()
            returnValue := mload(0)
        }
        return success && (returnSize == 0 ? address(token).code.length > 0 : returnValue == 1);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/Arrays.sol)
// This file was procedurally generated from scripts/generate/templates/Arrays.js.

pragma solidity ^0.8.20;

import {Comparators} from "./Comparators.sol";
import {SlotDerivation} from "./SlotDerivation.sol";
import {StorageSlot} from "./StorageSlot.sol";
import {Math} from "./math/Math.sol";

/**
 * @dev Collection of functions related to array types.
 */
library Arrays {
    using SlotDerivation for bytes32;
    using StorageSlot for bytes32;

    /**
     * @dev Sort an array of uint256 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        uint256[] memory array,
        function(uint256, uint256) pure returns (bool) comp
    ) internal pure returns (uint256[] memory) {
        _quickSort(_begin(array), _end(array), comp);
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of uint256 in increasing order.
     */
    function sort(uint256[] memory array) internal pure returns (uint256[] memory) {
        sort(array, Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of address (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        address[] memory array,
        function(address, address) pure returns (bool) comp
    ) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of address in increasing order.
     */
    function sort(address[] memory array) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of bytes32 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        bytes32[] memory array,
        function(bytes32, bytes32) pure returns (bool) comp
    ) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of bytes32 in increasing order.
     */
    function sort(bytes32[] memory array) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Performs a quick sort of a segment of memory. The segment sorted starts at `begin` (inclusive), and stops
     * at end (exclusive). Sorting follows the `comp` comparator.
     *
     * Invariant: `begin <= end`. This is the case when initially called by {sort} and is preserved in subcalls.
     *
     * IMPORTANT: Memory locations between `begin` and `end` are not validated/zeroed. This function should
     * be used only if the limits are within a memory array.
     */
    function _quickSort(uint256 begin, uint256 end, function(uint256, uint256) pure returns (bool) comp) private pure {
        unchecked {
            if (end - begin < 0x40) return;

            // Use first element as pivot
            uint256 pivot = _mload(begin);
            // Position where the pivot should be at the end of the loop
            uint256 pos = begin;

            for (uint256 it = begin + 0x20; it < end; it += 0x20) {
                if (comp(_mload(it), pivot)) {
                    // If the value stored at the iterator's position comes before the pivot, we increment the
                    // position of the pivot and move the value there.
                    pos += 0x20;
                    _swap(pos, it);
                }
            }

            _swap(begin, pos); // Swap pivot into place
            _quickSort(begin, pos, comp); // Sort the left side of the pivot
            _quickSort(pos + 0x20, end, comp); // Sort the right side of the pivot
        }
    }

    /**
     * @dev Pointer to the memory location of the first element of `array`.
     */
    function _begin(uint256[] memory array) private pure returns (uint256 ptr) {
        assembly ("memory-safe") {
            ptr := add(array, 0x20)
        }
    }

    /**
     * @dev Pointer to the memory location of the first memory word (32bytes) after `array`. This is the memory word
     * that comes just after the last element of the array.
     */
    function _end(uint256[] memory array) private pure returns (uint256 ptr) {
        unchecked {
            return _begin(array) + array.length * 0x20;
        }
    }

    /**
     * @dev Load memory word (as a uint256) at location `ptr`.
     */
    function _mload(uint256 ptr) private pure returns (uint256 value) {
        assembly {
            value := mload(ptr)
        }
    }

    /**
     * @dev Swaps the elements memory location `ptr1` and `ptr2`.
     */
    function _swap(uint256 ptr1, uint256 ptr2) private pure {
        assembly {
            let value1 := mload(ptr1)
            let value2 := mload(ptr2)
            mstore(ptr1, value2)
            mstore(ptr2, value1)
        }
    }

    /// @dev Helper: low level cast address memory array to uint256 memory array
    function _castToUint256Array(address[] memory input) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 memory array to uint256 memory array
    function _castToUint256Array(bytes32[] memory input) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast address comp function to uint256 comp function
    function _castToUint256Comp(
        function(address, address) pure returns (bool) input
    ) private pure returns (function(uint256, uint256) pure returns (bool) output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 comp function to uint256 comp function
    function _castToUint256Comp(
        function(bytes32, bytes32) pure returns (bool) input
    ) private pure returns (function(uint256, uint256) pure returns (bool) output) {
        assembly {
            output := input
        }
    }

    /**
     * @dev Searches a sorted `array` and returns the first index that contains
     * a value greater or equal to `element`. If no such index exists (i.e. all
     * values in the array are strictly less than `element`), the array length is
     * returned. Time complexity O(log n).
     *
     * NOTE: The `array` is expected to be sorted in ascending order, and to
     * contain no repeated elements.
     *
     * IMPORTANT: Deprecated. This implementation behaves as {lowerBound} but lacks
     * support for repeated elements in the array. The {lowerBound} function should
     * be used instead.
     */
    function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && unsafeAccess(array, low - 1).value == element) {
            return low - 1;
        } else {
            return low;
        }
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value greater or equal than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/lower_bound[lower_bound].
     */
    function lowerBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value strictly greater than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/upper_bound[upper_bound].
     */
    function upperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Same as {lowerBound}, but with an array in memory.
     */
    function lowerBoundMemory(uint256[] memory array, uint256 element) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Same as {upperBound}, but with an array in memory.
     */
    function upperBoundMemory(uint256[] memory array, uint256 element) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(address[] storage arr, uint256 pos) internal pure returns (StorageSlot.AddressSlot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getAddressSlot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(bytes32[] storage arr, uint256 pos) internal pure returns (StorageSlot.Bytes32Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getBytes32Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(uint256[] storage arr, uint256 pos) internal pure returns (StorageSlot.Uint256Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getUint256Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(address[] memory arr, uint256 pos) internal pure returns (address res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(bytes32[] memory arr, uint256 pos) internal pure returns (bytes32 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(uint256[] memory arr, uint256 pos) internal pure returns (uint256 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(address[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(bytes32[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(uint256[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Comparators.sol)

pragma solidity ^0.8.20;

/**
 * @dev Provides a set of functions to compare values.
 *
 * _Available since v5.1._
 */
library Comparators {
    function lt(uint256 a, uint256 b) internal pure returns (bool) {
        return a < b;
    }

    function gt(uint256 a, uint256 b) internal pure returns (bool) {
        return a > b;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.20;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS
    }

    /**
     * @dev The signature derives the `address(0)`.
     */
    error ECDSAInvalidSignature();

    /**
     * @dev The signature has an invalid length.
     */
    error ECDSAInvalidSignatureLength(uint256 length);

    /**
     * @dev The signature has an S value that is in the upper half order.
     */
    error ECDSAInvalidSignatureS(bytes32 s);

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with `signature` or an error. This will not
     * return address(0) without also returning an error description. Errors are documented using an enum (error type)
     * and a bytes32 providing additional information about the error.
     *
     * If no error is returned, then the address can be used for verification purposes.
     *
     * The `ecrecover` EVM precompile allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {MessageHashUtils-toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     */
    function tryRecover(
        bytes32 hash,
        bytes memory signature
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            assembly ("memory-safe") {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength, bytes32(signature.length));
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM precompile allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {MessageHashUtils-toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, signature);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[ERC-2098 short signatures]
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        unchecked {
            bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
            // We do not check for an overflow here since the shift operation results in 0 or 1.
            uint8 v = uint8((uint256(vs) >> 255) + 27);
            return tryRecover(hash, v, r, s);
        }
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, r, vs);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS, s);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature, bytes32(0));
        }

        return (signer, RecoverError.NoError, bytes32(0));
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, v, r, s);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Optionally reverts with the corresponding custom error according to the `error` argument provided.
     */
    function _throwError(RecoverError error, bytes32 errorArg) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert ECDSAInvalidSignature();
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert ECDSAInvalidSignatureLength(uint256(errorArg));
        } else if (error == RecoverError.InvalidSignatureS) {
            revert ECDSAInvalidSignatureS(errorArg);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.20;

import {MessageHashUtils} from "./MessageHashUtils.sol";
import {ShortStrings, ShortString} from "../ShortStrings.sol";
import {IERC5267} from "../../interfaces/IERC5267.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP-712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding scheme specified in the EIP requires a domain separator and a hash of the typed structured data, whose
 * encoding is very generic and therefore its implementation in Solidity is not feasible, thus this contract
 * does not implement the encoding itself. Protocols need to implement the type-specific encoding they need in order to
 * produce the hash of their typed data using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP-712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain
 * separator of the implementation contract. This will cause the {_domainSeparatorV4} function to always rebuild the
 * separator from the immutable values, which is cheaper than accessing a cached version in cold storage.
 *
 * @custom:oz-upgrades-unsafe-allow state-variable-immutable
 */
abstract contract EIP712 is IERC5267 {
    using ShortStrings for *;

    bytes32 private constant TYPE_HASH =
        keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _cachedDomainSeparator;
    uint256 private immutable _cachedChainId;
    address private immutable _cachedThis;

    bytes32 private immutable _hashedName;
    bytes32 private immutable _hashedVersion;

    ShortString private immutable _name;
    ShortString private immutable _version;
    // slither-disable-next-line constable-states
    string private _nameFallback;
    // slither-disable-next-line constable-states
    string private _versionFallback;

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP-712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        _name = name.toShortStringWithFallback(_nameFallback);
        _version = version.toShortStringWithFallback(_versionFallback);
        _hashedName = keccak256(bytes(name));
        _hashedVersion = keccak256(bytes(version));

        _cachedChainId = block.chainid;
        _cachedDomainSeparator = _buildDomainSeparator();
        _cachedThis = address(this);
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _cachedThis && block.chainid == _cachedChainId) {
            return _cachedDomainSeparator;
        } else {
            return _buildDomainSeparator();
        }
    }

    function _buildDomainSeparator() private view returns (bytes32) {
        return keccak256(abi.encode(TYPE_HASH, _hashedName, _hashedVersion, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return MessageHashUtils.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @inheritdoc IERC5267
     */
    function eip712Domain()
        public
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        return (
            hex"0f", // 01111
            _EIP712Name(),
            _EIP712Version(),
            block.chainid,
            address(this),
            bytes32(0),
            new uint256[](0)
        );
    }

    /**
     * @dev The name parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _name which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Name() internal view returns (string memory) {
        return _name.toStringWithFallback(_nameFallback);
    }

    /**
     * @dev The version parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _version which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Version() internal view returns (string memory) {
        return _version.toStringWithFallback(_versionFallback);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/cryptography/MessageHashUtils.sol)

pragma solidity ^0.8.20;

import {Strings} from "../Strings.sol";

/**
 * @dev Signature message hash utilities for producing digests to be consumed by {ECDSA} recovery or signing.
 *
 * The library provides methods for generating a hash of a message that conforms to the
 * https://eips.ethereum.org/EIPS/eip-191[ERC-191] and https://eips.ethereum.org/EIPS/eip-712[EIP 712]
 * specifications.
 */
library MessageHashUtils {
    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing a bytes32 `messageHash` with
     * `"\x19Ethereum Signed Message:\n32"` and hashing the result. It corresponds with the
     * hash signed when using the https://ethereum.org/en/developers/docs/apis/json-rpc/#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * NOTE: The `messageHash` parameter is intended to be the result of hashing a raw message with
     * keccak256, although any bytes32 value can be safely used because the final digest will
     * be re-hashed.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes32 messageHash) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            mstore(0x00, "\x19Ethereum Signed Message:\n32") // 32 is the bytes-length of messageHash
            mstore(0x1c, messageHash) // 0x1c (28) is the length of the prefix
            digest := keccak256(0x00, 0x3c) // 0x3c is the length of the prefix (0x1c) + messageHash (0x20)
        }
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing an arbitrary `message` with
     * `"\x19Ethereum Signed Message:\n" + len(message)` and hashing the result. It corresponds with the
     * hash signed when using the https://ethereum.org/en/developers/docs/apis/json-rpc/#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes memory message) internal pure returns (bytes32) {
        return
            keccak256(bytes.concat("\x19Ethereum Signed Message:\n", bytes(Strings.toString(message.length)), message));
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x00` (data with intended validator).
     *
     * The digest is calculated by prefixing an arbitrary `data` with `"\x19\x00"` and the intended
     * `validator` address. Then hashing the result.
     *
     * See {ECDSA-recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(hex"19_00", validator, data));
    }

    /**
     * @dev Variant of {toDataWithIntendedValidatorHash-address-bytes} optimized for cases where `data` is a bytes32.
     */
    function toDataWithIntendedValidatorHash(
        address validator,
        bytes32 messageHash
    ) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            mstore(0x00, hex"19_00")
            mstore(0x02, shl(96, validator))
            mstore(0x16, messageHash)
            digest := keccak256(0x00, 0x36)
        }
    }

    /**
     * @dev Returns the keccak256 digest of an EIP-712 typed data (ERC-191 version `0x01`).
     *
     * The digest is calculated from a `domainSeparator` and a `structHash`, by prefixing them with
     * `\x19\x01` and hashing the result. It corresponds to the hash signed by the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`] JSON-RPC method as part of EIP-712.
     *
     * See {ECDSA-recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            mstore(ptr, hex"19_01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            digest := keccak256(ptr, 0x42)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/introspection/IERC165.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[ERC].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[ERC section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "../Panic.sol";
import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Return the 512-bit addition of two uint256.
     *
     * The result is stored in two 256 variables such that sum = high * 2²⁵⁶ + low.
     */
    function add512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        assembly ("memory-safe") {
            low := add(a, b)
            high := lt(low, a)
        }
    }

    /**
     * @dev Return the 512-bit multiplication of two uint256.
     *
     * The result is stored in two 256 variables such that product = high * 2²⁵⁶ + low.
     */
    function mul512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        // 512-bit multiply [high low] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
        // the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
        // variables such that product = high * 2²⁵⁶ + low.
        assembly ("memory-safe") {
            let mm := mulmod(a, b, not(0))
            low := mul(a, b)
            high := sub(sub(mm, low), lt(mm, low))
        }
    }

    /**
     * @dev Returns the addition of two unsigned integers, with a success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            success = c >= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with a success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a - b;
            success = c <= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with a success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a * b;
            assembly ("memory-safe") {
                // Only true when the multiplication doesn't overflow
                // (c / a == b) || (a == 0)
                success := or(eq(div(c, a), b), iszero(a))
            }
            // equivalent to: success ? c : 0
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a success flag (no division by zero).
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `DIV` opcode returns zero when the denominator is 0.
                result := div(a, b)
            }
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a success flag (no division by zero).
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `MOD` opcode returns zero when the denominator is 0.
                result := mod(a, b)
            }
        }
    }

    /**
     * @dev Unsigned saturating addition, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingAdd(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryAdd(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Unsigned saturating subtraction, bounds to zero instead of overflowing.
     */
    function saturatingSub(uint256 a, uint256 b) internal pure returns (uint256) {
        (, uint256 result) = trySub(a, b);
        return result;
    }

    /**
     * @dev Unsigned saturating multiplication, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingMul(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryMul(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * SafeCast.toUint(condition));
        }
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(a < b, a, b);
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }

        // The following calculation ensures accurate ceiling division without overflow.
        // Since a is non-zero, (a - 1) / b will not overflow.
        // The largest possible result occurs when (a - 1) / b is type(uint256).max,
        // but the largest value we can obtain is type(uint256).max - 1, which happens
        // when a = type(uint256).max and b = 1.
        unchecked {
            return SafeCast.toUint(a > 0) * ((a - 1) / b + 1);
        }
    }

    /**
     * @dev Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     *
     * Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
     * Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);

            // Handle non-overflow cases, 256 by 256 division.
            if (high == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return low / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= high) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [high low].
            uint256 remainder;
            assembly ("memory-safe") {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                high := sub(high, gt(remainder, low))
                low := sub(low, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator.
            // Always >= 1. See https://cs.stackexchange.com/q/138556/92363.

            uint256 twos = denominator & (0 - denominator);
            assembly ("memory-safe") {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [high low] by twos.
                low := div(low, twos)

                // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from high into low.
            low |= high * twos;

            // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
            // works in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and high
            // is no longer required.
            result = low * inverse;
            return result;
        }
    }

    /**
     * @dev Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculates floor(x * y >> n) with full precision. Throws if result overflows a uint256.
     */
    function mulShr(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);
            if (high >= 1 << n) {
                Panic.panic(Panic.UNDER_OVERFLOW);
            }
            return (high << (256 - n)) | (low >> n);
        }
    }

    /**
     * @dev Calculates x * y >> n with full precision, following the selected rounding direction.
     */
    function mulShr(uint256 x, uint256 y, uint8 n, Rounding rounding) internal pure returns (uint256) {
        return mulShr(x, y, n) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, 1 << n) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, except 0.
     * If n is not a prime, then Z/nZ is not a field, and some elements might not be inversible.
     *
     * If the input value is not inversible, 0 is returned.
     *
     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Fermat's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`. See {invModPrime}.
     */
    function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
        unchecked {
            if (n == 0) return 0;

            // The inverse modulo is calculated using the Extended Euclidean Algorithm (iterative version)
            // Used to compute integers x and y such that: ax + ny = gcd(a, n).
            // When the gcd is 1, then the inverse of a modulo n exists and it's x.
            // ax + ny = 1
            // ax = 1 + (-y)n
            // ax ≡ 1 (mod n) # x is the inverse of a modulo n

            // If the remainder is 0 the gcd is n right away.
            uint256 remainder = a % n;
            uint256 gcd = n;

            // Therefore the initial coefficients are:
            // ax + ny = gcd(a, n) = n
            // 0a + 1n = n
            int256 x = 0;
            int256 y = 1;

            while (remainder != 0) {
                uint256 quotient = gcd / remainder;

                (gcd, remainder) = (
                    // The old remainder is the next gcd to try.
                    remainder,
                    // Compute the next remainder.
                    // Can't overflow given that (a % gcd) * (gcd // (a % gcd)) <= gcd
                    // where gcd is at most n (capped to type(uint256).max)
                    gcd - remainder * quotient
                );

                (x, y) = (
                    // Increment the coefficient of a.
                    y,
                    // Decrement the coefficient of n.
                    // Can overflow, but the result is casted to uint256 so that the
                    // next value of y is "wrapped around" to a value between 0 and n - 1.
                    x - y * int256(quotient)
                );
            }

            if (gcd != 1) return 0; // No inverse exists.
            return ternary(x < 0, n - uint256(-x), uint256(x)); // Wrap the result if it's negative.
        }
    }

    /**
     * @dev Variant of {invMod}. More efficient, but only works if `p` is known to be a prime greater than `2`.
     *
     * From https://en.wikipedia.org/wiki/Fermat%27s_little_theorem[Fermat's little theorem], we know that if p is
     * prime, then `a**(p-1) ≡ 1 mod p`. As a consequence, we have `a * a**(p-2) ≡ 1 mod p`, which means that
     * `a**(p-2)` is the modular multiplicative inverse of a in Fp.
     *
     * NOTE: this function does NOT check that `p` is a prime greater than `2`.
     */
    function invModPrime(uint256 a, uint256 p) internal view returns (uint256) {
        unchecked {
            return Math.modExp(a, p - 2, p);
        }
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m)
     *
     * Requirements:
     * - modulus can't be zero
     * - underlying staticcall to precompile must succeed
     *
     * IMPORTANT: The result is only valid if the underlying call succeeds. When using this function, make
     * sure the chain you're using it on supports the precompiled contract for modular exponentiation
     * at address 0x05 as specified in https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise,
     * the underlying function will succeed given the lack of a revert, but the result may be incorrectly
     * interpreted as 0.
     */
    function modExp(uint256 b, uint256 e, uint256 m) internal view returns (uint256) {
        (bool success, uint256 result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m).
     * It includes a success flag indicating if the operation succeeded. Operation will be marked as failed if trying
     * to operate modulo 0 or if the underlying precompile reverted.
     *
     * IMPORTANT: The result is only valid if the success flag is true. When using this function, make sure the chain
     * you're using it on supports the precompiled contract for modular exponentiation at address 0x05 as specified in
     * https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise, the underlying function will succeed given the lack
     * of a revert, but the result may be incorrectly interpreted as 0.
     */
    function tryModExp(uint256 b, uint256 e, uint256 m) internal view returns (bool success, uint256 result) {
        if (m == 0) return (false, 0);
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            // | Offset    | Content    | Content (Hex)                                                      |
            // |-----------|------------|--------------------------------------------------------------------|
            // | 0x00:0x1f | size of b  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x20:0x3f | size of e  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x40:0x5f | size of m  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x60:0x7f | value of b | 0x<.............................................................b> |
            // | 0x80:0x9f | value of e | 0x<.............................................................e> |
            // | 0xa0:0xbf | value of m | 0x<.............................................................m> |
            mstore(ptr, 0x20)
            mstore(add(ptr, 0x20), 0x20)
            mstore(add(ptr, 0x40), 0x20)
            mstore(add(ptr, 0x60), b)
            mstore(add(ptr, 0x80), e)
            mstore(add(ptr, 0xa0), m)

            // Given the result < m, it's guaranteed to fit in 32 bytes,
            // so we can use the memory scratch space located at offset 0.
            success := staticcall(gas(), 0x05, ptr, 0xc0, 0x00, 0x20)
            result := mload(0x00)
        }
    }

    /**
     * @dev Variant of {modExp} that supports inputs of arbitrary length.
     */
    function modExp(bytes memory b, bytes memory e, bytes memory m) internal view returns (bytes memory) {
        (bool success, bytes memory result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Variant of {tryModExp} that supports inputs of arbitrary length.
     */
    function tryModExp(
        bytes memory b,
        bytes memory e,
        bytes memory m
    ) internal view returns (bool success, bytes memory result) {
        if (_zeroBytes(m)) return (false, new bytes(0));

        uint256 mLen = m.length;

        // Encode call args in result and move the free memory pointer
        result = abi.encodePacked(b.length, e.length, mLen, b, e, m);

        assembly ("memory-safe") {
            let dataPtr := add(result, 0x20)
            // Write result on top of args to avoid allocating extra memory.
            success := staticcall(gas(), 0x05, dataPtr, mload(result), dataPtr, mLen)
            // Overwrite the length.
            // result.length > returndatasize() is guaranteed because returndatasize() == m.length
            mstore(result, mLen)
            // Set the memory pointer after the returned data.
            mstore(0x40, add(dataPtr, mLen))
        }
    }

    /**
     * @dev Returns whether the provided byte array is zero.
     */
    function _zeroBytes(bytes memory byteArray) private pure returns (bool) {
        for (uint256 i = 0; i < byteArray.length; ++i) {
            if (byteArray[i] != 0) {
                return false;
            }
        }
        return true;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
     * towards zero.
     *
     * This method is based on Newton's method for computing square roots; the algorithm is restricted to only
     * using integer operations.
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        unchecked {
            // Take care of easy edge cases when a == 0 or a == 1
            if (a <= 1) {
                return a;
            }

            // In this function, we use Newton's method to get a root of `f(x) := x² - a`. It involves building a
            // sequence x_n that converges toward sqrt(a). For each iteration x_n, we also define the error between
            // the current value as `ε_n = | x_n - sqrt(a) |`.
            //
            // For our first estimation, we consider `e` the smallest power of 2 which is bigger than the square root
            // of the target. (i.e. `2**(e-1) ≤ sqrt(a) < 2**e`). We know that `e ≤ 128` because `(2¹²⁸)² = 2²⁵⁶` is
            // bigger than any uint256.
            //
            // By noticing that
            // `2**(e-1) ≤ sqrt(a) < 2**e → (2**(e-1))² ≤ a < (2**e)² → 2**(2*e-2) ≤ a < 2**(2*e)`
            // we can deduce that `e - 1` is `log2(a) / 2`. We can thus compute `x_n = 2**(e-1)` using a method similar
            // to the msb function.
            uint256 aa = a;
            uint256 xn = 1;

            if (aa >= (1 << 128)) {
                aa >>= 128;
                xn <<= 64;
            }
            if (aa >= (1 << 64)) {
                aa >>= 64;
                xn <<= 32;
            }
            if (aa >= (1 << 32)) {
                aa >>= 32;
                xn <<= 16;
            }
            if (aa >= (1 << 16)) {
                aa >>= 16;
                xn <<= 8;
            }
            if (aa >= (1 << 8)) {
                aa >>= 8;
                xn <<= 4;
            }
            if (aa >= (1 << 4)) {
                aa >>= 4;
                xn <<= 2;
            }
            if (aa >= (1 << 2)) {
                xn <<= 1;
            }

            // We now have x_n such that `x_n = 2**(e-1) ≤ sqrt(a) < 2**e = 2 * x_n`. This implies ε_n ≤ 2**(e-1).
            //
            // We can refine our estimation by noticing that the middle of that interval minimizes the error.
            // If we move x_n to equal 2**(e-1) + 2**(e-2), then we reduce the error to ε_n ≤ 2**(e-2).
            // This is going to be our x_0 (and ε_0)
            xn = (3 * xn) >> 1; // ε_0 := | x_0 - sqrt(a) | ≤ 2**(e-2)

            // From here, Newton's method give us:
            // x_{n+1} = (x_n + a / x_n) / 2
            //
            // One should note that:
            // x_{n+1}² - a = ((x_n + a / x_n) / 2)² - a
            //              = ((x_n² + a) / (2 * x_n))² - a
            //              = (x_n⁴ + 2 * a * x_n² + a²) / (4 * x_n²) - a
            //              = (x_n⁴ + 2 * a * x_n² + a² - 4 * a * x_n²) / (4 * x_n²)
            //              = (x_n⁴ - 2 * a * x_n² + a²) / (4 * x_n²)
            //              = (x_n² - a)² / (2 * x_n)²
            //              = ((x_n² - a) / (2 * x_n))²
            //              ≥ 0
            // Which proves that for all n ≥ 1, sqrt(a) ≤ x_n
            //
            // This gives us the proof of quadratic convergence of the sequence:
            // ε_{n+1} = | x_{n+1} - sqrt(a) |
            //         = | (x_n + a / x_n) / 2 - sqrt(a) |
            //         = | (x_n² + a - 2*x_n*sqrt(a)) / (2 * x_n) |
            //         = | (x_n - sqrt(a))² / (2 * x_n) |
            //         = | ε_n² / (2 * x_n) |
            //         = ε_n² / | (2 * x_n) |
            //
            // For the first iteration, we have a special case where x_0 is known:
            // ε_1 = ε_0² / | (2 * x_0) |
            //     ≤ (2**(e-2))² / (2 * (2**(e-1) + 2**(e-2)))
            //     ≤ 2**(2*e-4) / (3 * 2**(e-1))
            //     ≤ 2**(e-3) / 3
            //     ≤ 2**(e-3-log2(3))
            //     ≤ 2**(e-4.5)
            //
            // For the following iterations, we use the fact that, 2**(e-1) ≤ sqrt(a) ≤ x_n:
            // ε_{n+1} = ε_n² / | (2 * x_n) |
            //         ≤ (2**(e-k))² / (2 * 2**(e-1))
            //         ≤ 2**(2*e-2*k) / 2**e
            //         ≤ 2**(e-2*k)
            xn = (xn + a / xn) >> 1; // ε_1 := | x_1 - sqrt(a) | ≤ 2**(e-4.5)  -- special case, see above
            xn = (xn + a / xn) >> 1; // ε_2 := | x_2 - sqrt(a) | ≤ 2**(e-9)    -- general case with k = 4.5
            xn = (xn + a / xn) >> 1; // ε_3 := | x_3 - sqrt(a) | ≤ 2**(e-18)   -- general case with k = 9
            xn = (xn + a / xn) >> 1; // ε_4 := | x_4 - sqrt(a) | ≤ 2**(e-36)   -- general case with k = 18
            xn = (xn + a / xn) >> 1; // ε_5 := | x_5 - sqrt(a) | ≤ 2**(e-72)   -- general case with k = 36
            xn = (xn + a / xn) >> 1; // ε_6 := | x_6 - sqrt(a) | ≤ 2**(e-144)  -- general case with k = 72

            // Because e ≤ 128 (as discussed during the first estimation phase), we know have reached a precision
            // ε_6 ≤ 2**(e-144) < 1. Given we're operating on integers, then we can ensure that xn is now either
            // sqrt(a) or sqrt(a) + 1.
            return xn - SafeCast.toUint(xn > a / xn);
        }
    }

    /**
     * @dev Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && result * result < a);
        }
    }

    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log2(uint256 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // If upper 8 bits of 16-bit half set, add 8 to result
        r |= SafeCast.toUint((x >> r) > 0xff) << 3;
        // If upper 4 bits of 8-bit half set, add 4 to result
        r |= SafeCast.toUint((x >> r) > 0xf) << 2;

        // Shifts value right by the current result and use it as an index into this lookup table:
        //
        // | x (4 bits) |  index  | table[index] = MSB position |
        // |------------|---------|-----------------------------|
        // |    0000    |    0    |        table[0] = 0         |
        // |    0001    |    1    |        table[1] = 0         |
        // |    0010    |    2    |        table[2] = 1         |
        // |    0011    |    3    |        table[3] = 1         |
        // |    0100    |    4    |        table[4] = 2         |
        // |    0101    |    5    |        table[5] = 2         |
        // |    0110    |    6    |        table[6] = 2         |
        // |    0111    |    7    |        table[7] = 2         |
        // |    1000    |    8    |        table[8] = 3         |
        // |    1001    |    9    |        table[9] = 3         |
        // |    1010    |   10    |        table[10] = 3        |
        // |    1011    |   11    |        table[11] = 3        |
        // |    1100    |   12    |        table[12] = 3        |
        // |    1101    |   13    |        table[13] = 3        |
        // |    1110    |   14    |        table[14] = 3        |
        // |    1111    |   15    |        table[15] = 3        |
        //
        // The lookup table is represented as a 32-byte value with the MSB positions for 0-15 in the last 16 bytes.
        assembly ("memory-safe") {
            r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030300000000000000000000000000000000))
        }
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << result < value);
        }
    }

    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 10 ** result < value);
        }
    }

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // Add 1 if upper 8 bits of 16-bit half set, and divide accumulated result by 8
        return (r >> 3) | SafeCast.toUint((x >> r) > 0xff);
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << (result << 3) < value);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.20;

/**
 * @dev Wrappers over Solidity's uintXX/intXX/bool casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeCast {
    /**
     * @dev Value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedIntToUint(int256 value);

    /**
     * @dev Value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedIntDowncast(uint8 bits, int256 value);

    /**
     * @dev An uint value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedUintToInt(uint256 value);

    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        if (value > type(uint248).max) {
            revert SafeCastOverflowedUintDowncast(248, value);
        }
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        if (value > type(uint240).max) {
            revert SafeCastOverflowedUintDowncast(240, value);
        }
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        if (value > type(uint232).max) {
            revert SafeCastOverflowedUintDowncast(232, value);
        }
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        if (value > type(uint224).max) {
            revert SafeCastOverflowedUintDowncast(224, value);
        }
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        if (value > type(uint216).max) {
            revert SafeCastOverflowedUintDowncast(216, value);
        }
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        if (value > type(uint208).max) {
            revert SafeCastOverflowedUintDowncast(208, value);
        }
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        if (value > type(uint200).max) {
            revert SafeCastOverflowedUintDowncast(200, value);
        }
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        if (value > type(uint192).max) {
            revert SafeCastOverflowedUintDowncast(192, value);
        }
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        if (value > type(uint184).max) {
            revert SafeCastOverflowedUintDowncast(184, value);
        }
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        if (value > type(uint176).max) {
            revert SafeCastOverflowedUintDowncast(176, value);
        }
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        if (value > type(uint168).max) {
            revert SafeCastOverflowedUintDowncast(168, value);
        }
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        if (value > type(uint160).max) {
            revert SafeCastOverflowedUintDowncast(160, value);
        }
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        if (value > type(uint152).max) {
            revert SafeCastOverflowedUintDowncast(152, value);
        }
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        if (value > type(uint144).max) {
            revert SafeCastOverflowedUintDowncast(144, value);
        }
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        if (value > type(uint136).max) {
            revert SafeCastOverflowedUintDowncast(136, value);
        }
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        if (value > type(uint128).max) {
            revert SafeCastOverflowedUintDowncast(128, value);
        }
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        if (value > type(uint120).max) {
            revert SafeCastOverflowedUintDowncast(120, value);
        }
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        if (value > type(uint112).max) {
            revert SafeCastOverflowedUintDowncast(112, value);
        }
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        if (value > type(uint104).max) {
            revert SafeCastOverflowedUintDowncast(104, value);
        }
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        if (value > type(uint96).max) {
            revert SafeCastOverflowedUintDowncast(96, value);
        }
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        if (value > type(uint88).max) {
            revert SafeCastOverflowedUintDowncast(88, value);
        }
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        if (value > type(uint80).max) {
            revert SafeCastOverflowedUintDowncast(80, value);
        }
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        if (value > type(uint72).max) {
            revert SafeCastOverflowedUintDowncast(72, value);
        }
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        if (value > type(uint64).max) {
            revert SafeCastOverflowedUintDowncast(64, value);
        }
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        if (value > type(uint56).max) {
            revert SafeCastOverflowedUintDowncast(56, value);
        }
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        if (value > type(uint48).max) {
            revert SafeCastOverflowedUintDowncast(48, value);
        }
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        if (value > type(uint40).max) {
            revert SafeCastOverflowedUintDowncast(40, value);
        }
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        if (value > type(uint32).max) {
            revert SafeCastOverflowedUintDowncast(32, value);
        }
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        if (value > type(uint24).max) {
            revert SafeCastOverflowedUintDowncast(24, value);
        }
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        if (value > type(uint16).max) {
            revert SafeCastOverflowedUintDowncast(16, value);
        }
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        if (value > type(uint8).max) {
            revert SafeCastOverflowedUintDowncast(8, value);
        }
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        if (value < 0) {
            revert SafeCastOverflowedIntToUint(value);
        }
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(248, value);
        }
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(240, value);
        }
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(232, value);
        }
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(224, value);
        }
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(216, value);
        }
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(208, value);
        }
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(200, value);
        }
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(192, value);
        }
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(184, value);
        }
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(176, value);
        }
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(168, value);
        }
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(160, value);
        }
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(152, value);
        }
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(144, value);
        }
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(136, value);
        }
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(128, value);
        }
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(120, value);
        }
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(112, value);
        }
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(104, value);
        }
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(96, value);
        }
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(88, value);
        }
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(80, value);
        }
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(72, value);
        }
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(64, value);
        }
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(56, value);
        }
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(48, value);
        }
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(40, value);
        }
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(32, value);
        }
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(24, value);
        }
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(16, value);
        }
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(8, value);
        }
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        if (value > uint256(type(int256).max)) {
            revert SafeCastOverflowedUintToInt(value);
        }
        return int256(value);
    }

    /**
     * @dev Cast a boolean (false or true) to a uint256 (0 or 1) with no jump.
     */
    function toUint(bool b) internal pure returns (uint256 u) {
        assembly ("memory-safe") {
            u := iszero(iszero(b))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, int256 a, int256 b) internal pure returns (int256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * int256(SafeCast.toUint(condition)));
        }
    }

    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a < b, a, b);
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // Formula from the "Bit Twiddling Hacks" by Sean Eron Anderson.
            // Since `n` is a signed integer, the generated bytecode will use the SAR opcode to perform the right shift,
            // taking advantage of the most significant (or "sign" bit) in two's complement representation.
            // This opcode adds new most significant bits set to the value of the previous most significant bit. As a result,
            // the mask will either be `bytes32(0)` (if n is positive) or `~bytes32(0)` (if n is negative).
            int256 mask = n >> 255;

            // A `bytes32(0)` mask leaves the input unchanged, while a `~bytes32(0)` mask complements it.
            return uint256((n + mask) ^ mask);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/Nonces.sol)
pragma solidity ^0.8.20;

/**
 * @dev Provides tracking nonces for addresses. Nonces will only increment.
 */
abstract contract Nonces {
    /**
     * @dev The nonce used for an `account` is not the expected current nonce.
     */
    error InvalidAccountNonce(address account, uint256 currentNonce);

    mapping(address account => uint256) private _nonces;

    /**
     * @dev Returns the next unused nonce for an address.
     */
    function nonces(address owner) public view virtual returns (uint256) {
        return _nonces[owner];
    }

    /**
     * @dev Consumes a nonce.
     *
     * Returns the current value and increments nonce.
     */
    function _useNonce(address owner) internal virtual returns (uint256) {
        // For each account, the nonce has an initial value of 0, can only be incremented by one, and cannot be
        // decremented or reset. This guarantees that the nonce never overflows.
        unchecked {
            // It is important to do x++ and not ++x here.
            return _nonces[owner]++;
        }
    }

    /**
     * @dev Same as {_useNonce} but checking that `nonce` is the next valid for `owner`.
     */
    function _useCheckedNonce(address owner, uint256 nonce) internal virtual {
        uint256 current = _useNonce(owner);
        if (nonce != current) {
            revert InvalidAccountNonce(owner, current);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Panic.sol)

pragma solidity ^0.8.20;

/**
 * @dev Helper library for emitting standardized panic codes.
 *
 * ```solidity
 * contract Example {
 *      using Panic for uint256;
 *
 *      // Use any of the declared internal constants
 *      function foo() { Panic.GENERIC.panic(); }
 *
 *      // Alternatively
 *      function foo() { Panic.panic(Panic.GENERIC); }
 * }
 * ```
 *
 * Follows the list from https://github.com/ethereum/solidity/blob/v0.8.24/libsolutil/ErrorCodes.h[libsolutil].
 *
 * _Available since v5.1._
 */
// slither-disable-next-line unused-state
library Panic {
    /// @dev generic / unspecified error
    uint256 internal constant GENERIC = 0x00;
    /// @dev used by the assert() builtin
    uint256 internal constant ASSERT = 0x01;
    /// @dev arithmetic underflow or overflow
    uint256 internal constant UNDER_OVERFLOW = 0x11;
    /// @dev division or modulo by zero
    uint256 internal constant DIVISION_BY_ZERO = 0x12;
    /// @dev enum conversion error
    uint256 internal constant ENUM_CONVERSION_ERROR = 0x21;
    /// @dev invalid encoding in storage
    uint256 internal constant STORAGE_ENCODING_ERROR = 0x22;
    /// @dev empty array pop
    uint256 internal constant EMPTY_ARRAY_POP = 0x31;
    /// @dev array out of bounds access
    uint256 internal constant ARRAY_OUT_OF_BOUNDS = 0x32;
    /// @dev resource error (too large allocation or too large array)
    uint256 internal constant RESOURCE_ERROR = 0x41;
    /// @dev calling invalid internal function
    uint256 internal constant INVALID_INTERNAL_FUNCTION = 0x51;

    /// @dev Reverts with a panic code. Recommended to use with
    /// the internal constants with predefined codes.
    function panic(uint256 code) internal pure {
        assembly ("memory-safe") {
            mstore(0x00, 0x4e487b71)
            mstore(0x20, code)
            revert(0x1c, 0x24)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/ShortStrings.sol)

pragma solidity ^0.8.20;

import {StorageSlot} from "./StorageSlot.sol";

// | string  | 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA   |
// | length  | 0x                                                              BB |
type ShortString is bytes32;

/**
 * @dev This library provides functions to convert short memory strings
 * into a `ShortString` type that can be used as an immutable variable.
 *
 * Strings of arbitrary length can be optimized using this library if
 * they are short enough (up to 31 bytes) by packing them with their
 * length (1 byte) in a single EVM word (32 bytes). Additionally, a
 * fallback mechanism can be used for every other case.
 *
 * Usage example:
 *
 * ```solidity
 * contract Named {
 *     using ShortStrings for *;
 *
 *     ShortString private immutable _name;
 *     string private _nameFallback;
 *
 *     constructor(string memory contractName) {
 *         _name = contractName.toShortStringWithFallback(_nameFallback);
 *     }
 *
 *     function name() external view returns (string memory) {
 *         return _name.toStringWithFallback(_nameFallback);
 *     }
 * }
 * ```
 */
library ShortStrings {
    // Used as an identifier for strings longer than 31 bytes.
    bytes32 private constant FALLBACK_SENTINEL = 0x00000000000000000000000000000000000000000000000000000000000000FF;

    error StringTooLong(string str);
    error InvalidShortString();

    /**
     * @dev Encode a string of at most 31 chars into a `ShortString`.
     *
     * This will trigger a `StringTooLong` error is the input string is too long.
     */
    function toShortString(string memory str) internal pure returns (ShortString) {
        bytes memory bstr = bytes(str);
        if (bstr.length > 31) {
            revert StringTooLong(str);
        }
        return ShortString.wrap(bytes32(uint256(bytes32(bstr)) | bstr.length));
    }

    /**
     * @dev Decode a `ShortString` back to a "normal" string.
     */
    function toString(ShortString sstr) internal pure returns (string memory) {
        uint256 len = byteLength(sstr);
        // using `new string(len)` would work locally but is not memory safe.
        string memory str = new string(32);
        assembly ("memory-safe") {
            mstore(str, len)
            mstore(add(str, 0x20), sstr)
        }
        return str;
    }

    /**
     * @dev Return the length of a `ShortString`.
     */
    function byteLength(ShortString sstr) internal pure returns (uint256) {
        uint256 result = uint256(ShortString.unwrap(sstr)) & 0xFF;
        if (result > 31) {
            revert InvalidShortString();
        }
        return result;
    }

    /**
     * @dev Encode a string into a `ShortString`, or write it to storage if it is too long.
     */
    function toShortStringWithFallback(string memory value, string storage store) internal returns (ShortString) {
        if (bytes(value).length < 32) {
            return toShortString(value);
        } else {
            StorageSlot.getStringSlot(store).value = value;
            return ShortString.wrap(FALLBACK_SENTINEL);
        }
    }

    /**
     * @dev Decode a string that was encoded to `ShortString` or written to storage using {toShortStringWithFallback}.
     */
    function toStringWithFallback(ShortString value, string storage store) internal pure returns (string memory) {
        if (ShortString.unwrap(value) != FALLBACK_SENTINEL) {
            return toString(value);
        } else {
            return store;
        }
    }

    /**
     * @dev Return the length of a string that was encoded to `ShortString` or written to storage using
     * {toShortStringWithFallback}.
     *
     * WARNING: This will return the "byte length" of the string. This may not reflect the actual length in terms of
     * actual characters as the UTF-8 encoding of a single character can span over multiple bytes.
     */
    function byteLengthWithFallback(ShortString value, string storage store) internal view returns (uint256) {
        if (ShortString.unwrap(value) != FALLBACK_SENTINEL) {
            return byteLength(value);
        } else {
            return bytes(store).length;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/SlotDerivation.sol)
// This file was procedurally generated from scripts/generate/templates/SlotDerivation.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for computing storage (and transient storage) locations from namespaces and deriving slots
 * corresponding to standard patterns. The derivation method for array and mapping matches the storage layout used by
 * the solidity language / compiler.
 *
 * See https://docs.soliditylang.org/en/v0.8.20/internals/layout_in_storage.html#mappings-and-dynamic-arrays[Solidity docs for mappings and dynamic arrays.].
 *
 * Example usage:
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using StorageSlot for bytes32;
 *     using SlotDerivation for bytes32;
 *
 *     // Declare a namespace
 *     string private constant _NAMESPACE = "<namespace>"; // eg. OpenZeppelin.Slot
 *
 *     function setValueInNamespace(uint256 key, address newValue) internal {
 *         _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value = newValue;
 *     }
 *
 *     function getValueInNamespace(uint256 key) internal view returns (address) {
 *         return _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {StorageSlot}.
 *
 * NOTE: This library provides a way to manipulate storage locations in a non-standard way. Tooling for checking
 * upgrade safety will ignore the slots accessed through this library.
 *
 * _Available since v5.1._
 */
library SlotDerivation {
    /**
     * @dev Derive an ERC-7201 slot from a string (namespace).
     */
    function erc7201Slot(string memory namespace) internal pure returns (bytes32 slot) {
        assembly ("memory-safe") {
            mstore(0x00, sub(keccak256(add(namespace, 0x20), mload(namespace)), 1))
            slot := and(keccak256(0x00, 0x20), not(0xff))
        }
    }

    /**
     * @dev Add an offset to a slot to get the n-th element of a structure or an array.
     */
    function offset(bytes32 slot, uint256 pos) internal pure returns (bytes32 result) {
        unchecked {
            return bytes32(uint256(slot) + pos);
        }
    }

    /**
     * @dev Derive the location of the first element in an array from the slot where the length is stored.
     */
    function deriveArray(bytes32 slot) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, slot)
            result := keccak256(0x00, 0x20)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, address key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, and(key, shr(96, not(0))))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bool key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, iszero(iszero(key)))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bytes32 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, uint256 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, int256 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, string memory key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bytes memory key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns a `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/Strings.sol)

pragma solidity ^0.8.20;

import {Math} from "./math/Math.sol";
import {SafeCast} from "./math/SafeCast.sol";
import {SignedMath} from "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    using SafeCast for *;

    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;
    uint256 private constant SPECIAL_CHARS_LOOKUP =
        (1 << 0x08) | // backspace
            (1 << 0x09) | // tab
            (1 << 0x0a) | // newline
            (1 << 0x0c) | // form feed
            (1 << 0x0d) | // carriage return
            (1 << 0x22) | // double quote
            (1 << 0x5c); // backslash

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev The string being parsed contains characters that are not in scope of the given base.
     */
    error StringsInvalidChar();

    /**
     * @dev The string being parsed is not a properly formatted address.
     */
    error StringsInvalidAddressFormat();

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            assembly ("memory-safe") {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                assembly ("memory-safe") {
                    mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        uint256 localValue = value;
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal
     * representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its checksummed ASCII `string` hexadecimal
     * representation, according to EIP-55.
     */
    function toChecksumHexString(address addr) internal pure returns (string memory) {
        bytes memory buffer = bytes(toHexString(addr));

        // hash the hex part of buffer (skip length + 2 bytes, length 40)
        uint256 hashValue;
        assembly ("memory-safe") {
            hashValue := shr(96, keccak256(add(buffer, 0x22), 40))
        }

        for (uint256 i = 41; i > 1; --i) {
            // possible values for buffer[i] are 48 (0) to 57 (9) and 97 (a) to 102 (f)
            if (hashValue & 0xf > 7 && uint8(buffer[i]) > 96) {
                // case shift by xoring with 0x20
                buffer[i] ^= 0x20;
            }
            hashValue >>= 4;
        }
        return string(buffer);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
    }

    /**
     * @dev Parse a decimal string and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input) internal pure returns (uint256) {
        return parseUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        uint256 result = 0;
        for (uint256 i = begin; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 9) return (false, 0);
            result *= 10;
            result += chr;
        }
        return (true, result);
    }

    /**
     * @dev Parse a decimal string and returns the value as a `int256`.
     *
     * Requirements:
     * - The string must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input) internal pure returns (int256) {
        return parseInt(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseInt-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input, uint256 begin, uint256 end) internal pure returns (int256) {
        (bool success, int256 value) = tryParseInt(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseInt-string} that returns false if the parsing fails because of an invalid character or if
     * the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(string memory input) internal pure returns (bool success, int256 value) {
        return _tryParseIntUncheckedBounds(input, 0, bytes(input).length);
    }

    uint256 private constant ABS_MIN_INT256 = 2 ** 255;

    /**
     * @dev Variant of {parseInt-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character or if the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, int256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseIntUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseInt-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseIntUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, int256 value) {
        bytes memory buffer = bytes(input);

        // Check presence of a negative sign.
        bytes1 sign = begin == end ? bytes1(0) : bytes1(_unsafeReadBytesOffset(buffer, begin)); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        bool positiveSign = sign == bytes1("+");
        bool negativeSign = sign == bytes1("-");
        uint256 offset = (positiveSign || negativeSign).toUint();

        (bool absSuccess, uint256 absValue) = tryParseUint(input, begin + offset, end);

        if (absSuccess && absValue < ABS_MIN_INT256) {
            return (true, negativeSign ? -int256(absValue) : int256(absValue));
        } else if (absSuccess && negativeSign && absValue == ABS_MIN_INT256) {
            return (true, type(int256).min);
        } else return (false, 0);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input) internal pure returns (uint256) {
        return parseHexUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseHexUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseHexUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseHexUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string-uint256-uint256} that returns false if the parsing fails because of an
     * invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseHexUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseHexUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseHexUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        // skip 0x prefix if present
        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(buffer, begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 offset = hasPrefix.toUint() * 2;

        uint256 result = 0;
        for (uint256 i = begin + offset; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 15) return (false, 0);
            result *= 16;
            unchecked {
                // Multiplying by 16 is equivalent to a shift of 4 bits (with additional overflow check).
                // This guarantees that adding a value < 16 will not cause an overflow, hence the unchecked.
                result += chr;
            }
        }
        return (true, result);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as an `address`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input) internal pure returns (address) {
        return parseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input, uint256 begin, uint256 end) internal pure returns (address) {
        (bool success, address value) = tryParseAddress(input, begin, end);
        if (!success) revert StringsInvalidAddressFormat();
        return value;
    }

    /**
     * @dev Variant of {parseAddress-string} that returns false if the parsing fails because the input is not a properly
     * formatted address. See {parseAddress-string} requirements.
     */
    function tryParseAddress(string memory input) internal pure returns (bool success, address value) {
        return tryParseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string-uint256-uint256} that returns false if the parsing fails because input is not a properly
     * formatted address. See {parseAddress-string-uint256-uint256} requirements.
     */
    function tryParseAddress(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, address value) {
        if (end > bytes(input).length || begin > end) return (false, address(0));

        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(bytes(input), begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 expectedLength = 40 + hasPrefix.toUint() * 2;

        // check that input is the correct length
        if (end - begin == expectedLength) {
            // length guarantees that this does not overflow, and value is at most type(uint160).max
            (bool s, uint256 v) = _tryParseHexUintUncheckedBounds(input, begin, end);
            return (s, address(uint160(v)));
        } else {
            return (false, address(0));
        }
    }

    function _tryParseChr(bytes1 chr) private pure returns (uint8) {
        uint8 value = uint8(chr);

        // Try to parse `chr`:
        // - Case 1: [0-9]
        // - Case 2: [a-f]
        // - Case 3: [A-F]
        // - otherwise not supported
        unchecked {
            if (value > 47 && value < 58) value -= 48;
            else if (value > 96 && value < 103) value -= 87;
            else if (value > 64 && value < 71) value -= 55;
            else return type(uint8).max;
        }

        return value;
    }

    /**
     * @dev Escape special characters in JSON strings. This can be useful to prevent JSON injection in NFT metadata.
     *
     * WARNING: This function should only be used in double quoted JSON strings. Single quotes are not escaped.
     *
     * NOTE: This function escapes all unicode characters, and not just the ones in ranges defined in section 2.5 of
     * RFC-4627 (U+0000 to U+001F, U+0022 and U+005C). ECMAScript's `JSON.parse` does recover escaped unicode
     * characters that are not in this range, but other tooling may provide different results.
     */
    function escapeJSON(string memory input) internal pure returns (string memory) {
        bytes memory buffer = bytes(input);
        bytes memory output = new bytes(2 * buffer.length); // worst case scenario
        uint256 outputLength = 0;

        for (uint256 i; i < buffer.length; ++i) {
            bytes1 char = bytes1(_unsafeReadBytesOffset(buffer, i));
            if (((SPECIAL_CHARS_LOOKUP & (1 << uint8(char))) != 0)) {
                output[outputLength++] = "\\";
                if (char == 0x08) output[outputLength++] = "b";
                else if (char == 0x09) output[outputLength++] = "t";
                else if (char == 0x0a) output[outputLength++] = "n";
                else if (char == 0x0c) output[outputLength++] = "f";
                else if (char == 0x0d) output[outputLength++] = "r";
                else if (char == 0x5c) output[outputLength++] = "\\";
                else if (char == 0x22) {
                    // solhint-disable-next-line quotes
                    output[outputLength++] = '"';
                }
            } else {
                output[outputLength++] = char;
            }
        }
        // write the actual length and deallocate unused memory
        assembly ("memory-safe") {
            mstore(output, outputLength)
            mstore(0x40, add(output, shl(5, shr(5, add(outputLength, 63)))))
        }

        return string(output);
    }

    /**
     * @dev Reads a bytes32 from a bytes array without bounds checking.
     *
     * NOTE: making this function internal would mean it could be used with memory unsafe offset, and marking the
     * assembly block as such would prevent some optimizations.
     */
    function _unsafeReadBytesOffset(bytes memory buffer, uint256 offset) private pure returns (bytes32 value) {
        // This is not memory safe in the general case, but all calls to this private function are within bounds.
        assembly ("memory-safe") {
            value := mload(add(buffer, add(0x20, offset)))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/structs/EnumerableSet.sol)
// This file was procedurally generated from scripts/generate/templates/EnumerableSet.js.

pragma solidity ^0.8.20;

import {Arrays} from "../Arrays.sol";

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 * - Set can be cleared (all elements removed) in O(n).
 *
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 *
 * [WARNING]
 * ====
 * Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
 * unusable.
 * See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 * In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an
 * array of EnumerableSet.
 * ====
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position is the index of the value in the `values` array plus 1.
        // Position 0 is used to mean a value is not in the set.
        mapping(bytes32 value => uint256) _positions;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._positions[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We cache the value's position to prevent multiple reads from the same storage slot
        uint256 position = set._positions[value];

        if (position != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 valueIndex = position - 1;
            uint256 lastIndex = set._values.length - 1;

            if (valueIndex != lastIndex) {
                bytes32 lastValue = set._values[lastIndex];

                // Move the lastValue to the index where the value to delete is
                set._values[valueIndex] = lastValue;
                // Update the tracked position of the lastValue (that was just moved)
                set._positions[lastValue] = position;
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the tracked position for the deleted slot
            delete set._positions[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes all the values from a set. O(n).
     *
     * WARNING: Developers should keep in mind that this function has an unbounded cost and using it may render the
     * function uncallable if the set grows to the point where clearing it consumes too much gas to fit in a block.
     */
    function _clear(Set storage set) private {
        uint256 len = _length(set);
        for (uint256 i = 0; i < len; ++i) {
            delete set._positions[set._values[i]];
        }
        Arrays.unsafeSetLength(set._values, 0);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._positions[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Removes all the values from a set. O(n).
     *
     * WARNING: Developers should keep in mind that this function has an unbounded cost and using it may render the
     * function uncallable if the set grows to the point where clearing it consumes too much gas to fit in a block.
     */
    function clear(Bytes32Set storage set) internal {
        _clear(set._inner);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        bytes32[] memory store = _values(set._inner);
        bytes32[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes all the values from a set. O(n).
     *
     * WARNING: Developers should keep in mind that this function has an unbounded cost and using it may render the
     * function uncallable if the set grows to the point where clearing it consumes too much gas to fit in a block.
     */
    function clear(AddressSet storage set) internal {
        _clear(set._inner);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Removes all the values from a set. O(n).
     *
     * WARNING: Developers should keep in mind that this function has an unbounded cost and using it may render the
     * function uncallable if the set grows to the point where clearing it consumes too much gas to fit in a block.
     */
    function clear(UintSet storage set) internal {
        _clear(set._inner);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.25;

import { IERC20, IERC20Metadata, ERC20 } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { Ownable } from "@openzeppelin/contracts/access/Ownable.sol";
import { IFHERC20, FHERC20 } from "./FHERC20.sol";
import { euint128, FHE } from "@fhenixprotocol/cofhe-contracts/FHE.sol";
import { EnumerableSet } from "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";
import { SafeCast } from "@openzeppelin/contracts/utils/math/SafeCast.sol";

abstract contract ConfidentialClaim {
    using EnumerableSet for EnumerableSet.UintSet;

    struct Claim {
        uint256 ctHash;
        uint128 requestedAmount;
        uint128 decryptedAmount;
        bool decrypted;
        address to;
        bool claimed;
    }

    mapping(uint256 ctHash => Claim) private _claims;
    mapping(address => EnumerableSet.UintSet) private _userClaims;

    error ClaimNotFound();
    error AlreadyClaimed();

    function _createClaim(address to, uint128 value, euint128 claimable) internal {
        _claims[euint128.unwrap(claimable)] = Claim({
            ctHash: euint128.unwrap(claimable),
            requestedAmount: value,
            decryptedAmount: 0,
            decrypted: false,
            to: to,
            claimed: false
        });
        _userClaims[to].add(euint128.unwrap(claimable));
    }

    function _handleClaim(uint256 ctHash) internal returns (Claim memory claim) {
        claim = _claims[ctHash];

        // Check that the claimable amount exists and has not been claimed yet
        if (claim.to == address(0)) revert ClaimNotFound();
        if (claim.claimed) revert AlreadyClaimed();

        // Get the decrypted amount (reverts if the amount is not decrypted yet)
        uint128 amount = SafeCast.toUint128(FHE.getDecryptResult(ctHash));

        // Update the claim
        claim.decryptedAmount = amount;
        claim.decrypted = true;
        claim.claimed = true;

        // Update the claim in storage
        _claims[ctHash] = claim;

        // Remove the claimable amount from the user's claimable set
        _userClaims[claim.to].remove(ctHash);
    }

    function _handleClaimAll() internal returns (Claim[] memory claims) {
        claims = new Claim[](_userClaims[msg.sender].length());

        uint256[] memory ctHashes = _userClaims[msg.sender].values();
        for (uint256 i = 0; i < ctHashes.length; i++) {
            claims[i] = _handleClaim(ctHashes[i]);
        }
    }

    function getClaim(uint256 ctHash) public view returns (Claim memory) {
        Claim memory _claim = _claims[ctHash];
        (uint256 amount, bool decrypted) = FHE.getDecryptResultSafe(ctHash);
        _claim.decryptedAmount = SafeCast.toUint128(amount);
        _claim.decrypted = decrypted;
        return _claim;
    }

    function getUserClaims(address user) public view returns (Claim[] memory) {
        uint256[] memory ctHashes = _userClaims[user].values();
        Claim[] memory userClaims = new Claim[](ctHashes.length);
        for (uint256 i = 0; i < ctHashes.length; i++) {
            userClaims[i] = _claims[ctHashes[i]];
            (uint256 amount, bool decrypted) = FHE.getDecryptResultSafe(ctHashes[i]);
            userClaims[i].decryptedAmount = SafeCast.toUint128(amount);
            userClaims[i].decrypted = decrypted;
        }
        return userClaims;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.25;

import { ERC20 } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { IERC20Errors } from "@openzeppelin/contracts/interfaces/draft-IERC6093.sol";
import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { Context } from "@openzeppelin/contracts/utils/Context.sol";
import { EIP712 } from "@openzeppelin/contracts/utils/cryptography/EIP712.sol";
import { Nonces } from "@openzeppelin/contracts/utils/Nonces.sol";
import { ECDSA } from "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import { IFHERC20 } from "./interfaces/IFHERC20.sol";
import { IFHERC20Errors } from "./interfaces/IFHERC20Errors.sol";
import { FHE, euint128, InEuint128, Utils } from "@fhenixprotocol/cofhe-contracts/FHE.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 *
 * Note: This FHERC20 does not include FHE operations, and is intended to decouple the
 * frontend work from the active CoFHE (FHE Coprocessor) work during development and auditing.
 */
abstract contract FHERC20 is IFHERC20, IFHERC20Errors, Context, EIP712, Nonces {
    // NOTE: `indicatedBalances` are intended to indicate movement and change
    // of an encrypted FHERC20 balance, without exposing any encrypted data.
    //
    // !! WARNING !! These indicated balances MUST NOT be used in any FHERC20 logic, only
    // the encrypted balance should be used.
    //
    // `indicatedBalance` is implemented to make FHERC20s maximally backwards
    // compatible with existing ERC20 expectations.
    //
    // `indicatedBalance` is internally represented by a number between 0 and 99999.
    // When viewed in a wallet, it is transformed into a decimal value with 4 digits
    // of precision (0.0000 to 0.9999). These same increments are used as the
    // value in any emitted events. If the user has not interacted with this FHERC20
    // their indicated amount will be 0. Their first interaction will set the amount to
    // the midpoint (0.5000), and each subsequent interaction will shift that value by
    // the increment (0.0001). This gives room for up to 5000 interactions in either
    // direction, which is sufficient for >99.99% of user use cases.
    //
    // These `indicatedBalance` changes will show up in:
    // - transactions and block scanners (0xAAA -> 0xBBB - 0.0001 eETH)
    // - wallets and portfolios (eETH - 0.5538)
    //
    // `indicatedBalance` is included in the FHERC20 standard as a stop-gap
    // to indicate change when the real encrypted change is not yet implemented
    // in infrastructure like wallets and etherscans.
    mapping(address account => uint16) internal _indicatedBalances;
    mapping(address account => euint128) private _encBalances;

    uint16 internal _indicatedTotalSupply;
    euint128 private _encTotalSupply;

    string private _name;
    string private _symbol;
    uint8 private _decimals;
    uint256 private _indicatorTick;

    // EIP712 Permit

    bytes32 private constant PERMIT_TYPEHASH =
        keccak256("Permit(address owner,address spender,uint256 value_hash,uint256 nonce,uint256 deadline)");

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_, uint8 decimals_) EIP712(name_, "1") {
        _name = name_;
        _symbol = symbol_;
        _decimals = decimals_;

        _indicatorTick = decimals_ <= 4 ? 1 : 10 ** (decimals_ - 4);
    }

    /**
     * @dev Returns true if the token is a FHERC20.
     */
    function isFherc20() public view virtual returns (bool) {
        return true;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return _decimals;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     *
     * Returns the indicated total supply.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _indicatedTotalSupply * _indicatorTick;
    }

    /**
     * @dev Returns the encrypted total supply.
     */
    function encTotalSupply() public view virtual returns (euint128) {
        return _encTotalSupply;
    }

    /**
     * @dev Returns an flag indicating that the public balances returned by
     * `balanceOf` is an indication of the underlying encrypted balance.
     * The value returned is between 0.0000 and 0.9999, and
     * acts as a counter of tokens transfers and changes.
     *
     * Receiving tokens increments this indicator by +0.0001.
     * Sending tokens decrements the indicator by -0.0001.
     */
    function balanceOfIsIndicator() public view virtual returns (bool) {
        return true;
    }

    /**
     * @dev Returns the true size of the indicator tick
     */
    function indicatorTick() public view returns (uint256) {
        return _indicatorTick;
    }

    /**
     * @dev Returns an indicator of the underlying encrypted balance.
     * The value returned is [0](no interaction) / [0.0001 - 0.9999](indicated)
     * Indicator acts as a counter of tokens transfers and changes.
     *
     * Receiving tokens increments this indicator by +0.0001.
     * Sending tokens decrements the indicator by -0.0001.
     *
     * Returned in the decimal expectation of the token.
     */
    function balanceOf(address account) public view virtual returns (uint256) {
        return _indicatedBalances[account] * _indicatorTick;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     *
     * Returns the euint128 representing the account's true balance (encrypted)
     */
    function encBalanceOf(address account) public view virtual returns (euint128) {
        return _encBalances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20
     */
    function transfer(address, uint256) public pure returns (bool) {
        revert FHERC20IncompatibleFunction();
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Intended to be used as a EOA call with an encrypted input `InEuint128 inValue`.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     * - `inValue` must be a `InEuint128` to preserve confidentiality.
     */
    function encTransfer(address to, InEuint128 memory inValue) public virtual returns (euint128 transferred) {
        return encTransfer(to, FHE.asEuint128(inValue));
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Intended to be used as part of a contract call.
     * Ensure that `value` is allowed to be used by using `FHE.allow` with this contracts address.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     * - `value` must be a `euint128` to preserve confidentiality.
     */
    function encTransfer(address to, euint128 value) public virtual returns (euint128 transferred) {
        address owner = _msgSender();
        transferred = _transfer(owner, to, value);
    }

    /**
     * @dev See {IERC20-allowance}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20.
     * Allowances have been removed from FHERC20s to prevent encrypted balance leakage.
     * Allowances have been replaced with an EIP712 permit for each `encTransferFrom`.
     */
    function allowance(address, address) external pure returns (uint256) {
        revert FHERC20IncompatibleFunction();
    }

    /**
     * @dev See {IERC20-approve}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20.
     * Allowances have been removed from FHERC20s to prevent encrypted balance leakage.
     * Allowances have been replaced with an EIP712 permit for each `encTransferFrom`.
     */
    function approve(address, uint256) external pure returns (bool) {
        revert FHERC20IncompatibleFunction();
    }

    /**
     * @dev See {IERC20-transferFrom}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20
     */
    function transferFrom(address, address, uint256) public pure returns (bool) {
        revert FHERC20IncompatibleFunction();
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function encTransferFrom(
        address from,
        address to,
        InEuint128 memory inValue,
        FHERC20_EIP712_Permit calldata permit
    ) public virtual returns (euint128 transferred) {
        if (block.timestamp > permit.deadline) revert ERC2612ExpiredSignature(permit.deadline);

        if (from != permit.owner) revert FHERC20EncTransferFromOwnerMismatch(from, permit.owner);
        if (msg.sender != permit.spender) revert FHERC20EncTransferFromSpenderMismatch(msg.sender, permit.spender);

        if (inValue.ctHash != permit.value_hash)
            revert FHERC20EncTransferFromValueHashMismatch(inValue.ctHash, permit.value_hash);

        bytes32 structHash = keccak256(
            abi.encode(
                PERMIT_TYPEHASH,
                permit.owner,
                permit.spender,
                permit.value_hash,
                _useNonce(permit.owner),
                permit.deadline
            )
        );

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, permit.v, permit.r, permit.s);
        if (signer != permit.owner) {
            revert ERC2612InvalidSigner(signer, permit.owner);
        }

        euint128 value = FHE.asEuint128(inValue);

        transferred = _transfer(from, to, value);
    }

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _transfer(address from, address to, euint128 value) internal returns (euint128 transferred) {
        if (from == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        if (to == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        transferred = _update(from, to, value);
    }

    /*
     * @dev Increments a user's balance indicator by 0.0001
     */
    function _incrementIndicator(uint16 current) internal pure returns (uint16) {
        if (current == 0 || current == 9999) return 5001;
        return current + 1;
    }

    /*
     * @dev Decrements a user's balance indicator by 0.0001
     */
    function _decrementIndicator(uint16 value) internal pure returns (uint16) {
        if (value == 0 || value == 1) return 4999;
        return value - 1;
    }

    /**
     * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
     * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
     * this function.
     *
     * Emits a {Transfer} event and an {EncTransfer} event which includes the encrypted value.
     */
    function _update(address from, address to, euint128 value) internal virtual returns (euint128 transferred) {
        // If `value` is greater than the user's encBalance, it is replaced with 0
        // The transaction will succeed, but the amount transferred may be 0
        // Both `from` and `to` will have their `encBalance` updated in either case to preserve confidentiality
        //
        // NOTE: If the function is `_mint`, `from` is the zero address, and does not have an `encBalance` to
        //       compare against, so this check is skipped.
        if (from != address(0)) {
            transferred = FHE.select(value.lte(_encBalances[from]), value, FHE.asEuint128(0));
        } else {
            transferred = value;
        }

        if (from == address(0)) {
            _indicatedTotalSupply = _incrementIndicator(_indicatedTotalSupply);
            _encTotalSupply = FHE.add(_encTotalSupply, transferred);
        } else {
            _encBalances[from] = FHE.sub(_encBalances[from], transferred);
            _indicatedBalances[from] = _decrementIndicator(_indicatedBalances[from]);
        }

        if (to == address(0)) {
            _indicatedTotalSupply = _decrementIndicator(_indicatedTotalSupply);
            _encTotalSupply = FHE.sub(_encTotalSupply, transferred);
        } else {
            _encBalances[to] = FHE.add(_encBalances[to], transferred);
            _indicatedBalances[to] = _incrementIndicator(_indicatedBalances[to]);
        }

        // Update CoFHE Access Control List (ACL) to allow decrypting / sealing of the new balances
        if (euint128.unwrap(_encBalances[from]) != 0) {
            FHE.allowThis(_encBalances[from]);
            FHE.allow(_encBalances[from], from);
            FHE.allow(transferred, from);
        }
        if (euint128.unwrap(_encBalances[to]) != 0) {
            FHE.allowThis(_encBalances[to]);
            FHE.allow(_encBalances[to], to);
            FHE.allow(transferred, to);
        }

        // Allow the caller to decrypt the transferred amount
        FHE.allow(transferred, msg.sender);

        // Allow the total supply to be decrypted by anyone
        FHE.allowGlobal(_encTotalSupply);

        emit Transfer(from, to, _indicatorTick);
        emit EncTransfer(from, to, euint128.unwrap(transferred));
    }

    /**
     * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
     * Relies on the `_update` mechanism
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _mint(address account, uint128 value) internal returns (euint128 transferred) {
        if (account == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        transferred = _update(address(0), account, FHE.asEuint128(value));
    }

    /**
     * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
     * Relies on the `_update` mechanism.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead
     */
    function _burn(address account, uint128 value) internal returns (euint128 transferred) {
        if (account == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        transferred = _update(account, address(0), FHE.asEuint128(value));
    }

    // EIP712 Permit

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) public view override(IFHERC20, Nonces) returns (uint256) {
        return super.nonces(owner);
    }

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view virtual returns (bytes32) {
        return _domainSeparatorV4();
    }

    // FHERC20

    function resetIndicatedBalance() external {
        _indicatedBalances[msg.sender] = 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.25;

import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { euint128, InEuint128 } from "@fhenixprotocol/cofhe-contracts/FHE.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 *
 * Note: This FHERC20 does not include FHE operations, and is intended to decouple the
 * frontend work from the active CoFHE (FHE Coprocessor) work during development and auditing.
 */
interface IFHERC20 is IERC20, IERC20Metadata {
    /**
     * @dev EIP712 Permit reusable struct
     */
    struct FHERC20_EIP712_Permit {
        address owner;
        address spender;
        uint256 value_hash;
        uint256 deadline;
        uint8 v;
        bytes32 r;
        bytes32 s;
    }

    /**
     * @dev Emitted when `value_hash` encrypted tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event EncTransfer(address indexed from, address indexed to, uint256 value_hash);

    /**
     * @dev Returns true if the token is a FHERC20.
     */
    function isFherc20() external view returns (bool);

    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() external view returns (uint8);

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns an flag indicating that the external balances returned by
     * `balanceOf` is an indication of the underlying encrypted balance.
     * The value returned is between 0.0000 and 0.9999, and
     * acts as a counter of tokens transfers and changes.
     *
     * Receiving tokens increments this indicator by +0.0001.
     * Sending tokens decrements the indicator by -0.0001.
     */
    function balanceOfIsIndicator() external view returns (bool);

    /**
     * @dev Returns the true size of the indicator tick
     */
    function indicatorTick() external view returns (uint256);

    /**
     * @dev Returns an indicator of the underlying encrypted balance.
     * The value returned is [0](no interaction) / [0.0001 - 0.9999](indicated)
     * Indicator acts as a counter of tokens transfers and changes.
     *
     * Receiving tokens increments this indicator by +0.0001.
     * Sending tokens decrements the indicator by -0.0001.
     *
     * Returned in the decimal expectation of the token.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev See {IERC20-balanceOf}.
     *
     * Returns the euint128 representing the account's true balance (encrypted)
     */
    function encBalanceOf(address account) external view returns (euint128);

    /**
     * @dev See {IERC20-transfer}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20
     */
    function transfer(address, uint256) external pure returns (bool);

    /**
     * @dev See {IERC20-transfer}.
     *
     * Intended to be used as a EOA call with an encrypted input `InEuint128 inValue`.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     * - `inValue` must be a `InEuint128` to preserve confidentiality.
     */
    function encTransfer(address to, InEuint128 memory inValue) external returns (euint128 transferred);

    /**
     * @dev See {IERC20-transfer}.
     *
     * Intended to be used as part of a contract call.
     * Ensure that `value` is allowed to be used by using `FHE.allow` with this contracts address.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     * - `value` must be a `euint128` to preserve confidentiality.
     */
    function encTransfer(address to, euint128 value) external returns (euint128 transferred);

    /**
     * @dev See {IERC20-allowance}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20.
     * Allowances have been removed from FHERC20s to prevent encrypted balance leakage.
     * Allowances have been replaced with an EIP712 permit for each `encTransferFrom`.
     */
    function allowance(address, address) external pure returns (uint256);

    /**
     * @dev See {IERC20-approve}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20.
     * Allowances have been removed from FHERC20s to prevent encrypted balance leakage.
     * Allowances have been replaced with an EIP712 permit for each `encTransferFrom`.
     */
    function approve(address, uint256) external pure returns (bool);

    /**
     * @dev See {IERC20-transferFrom}.
     * Always reverts to prevent FHERC20 from being unintentionally treated as an ERC20
     */
    function transferFrom(address, address, uint256) external pure returns (bool);

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function encTransferFrom(
        address from,
        address to,
        InEuint128 memory inValue,
        FHERC20_EIP712_Permit calldata permit
    ) external returns (euint128 transferred);

    // EIP712 Permit

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);
    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.25;

import { IERC20Errors } from "@openzeppelin/contracts/interfaces/draft-IERC6093.sol";

/**
 * @dev Standard FHERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IFHERC20Errors is IERC20Errors {
    /**
     * @dev Indicates an incompatible function being called.
     * Prevents unintentional treatment of an FHERC20 as a cleartext ERC20
     */
    error FHERC20IncompatibleFunction();

    /**
     * @dev encTransferFrom `from` and `permit.owner` don't match
     * @param from encTransferFrom param.
     * @param permitOwner token owner included in FHERC20_EIP712_Permit struct.
     */
    error FHERC20EncTransferFromOwnerMismatch(address from, address permitOwner);

    /**
     * @dev encTransferFrom `to` and `permit.spender` don't match
     * @param to encTransferFrom param.
     * @param permitSpender token receiver included in FHERC20_EIP712_Permit struct.
     */
    error FHERC20EncTransferFromSpenderMismatch(address to, address permitSpender);

    /**
     * @dev encTransferFrom `value` greater than `permit.value_hash` dont match (permit doesn't match InEuint128)
     * @param inValueHash encTransferFrom param inValue.ctHash.
     * @param permitValueHash token amount hash included in FHERC20_EIP712_Permit struct.
     */
    error FHERC20EncTransferFromValueHashMismatch(uint256 inValueHash, uint256 permitValueHash);

    /**
     * @dev Permit deadline has expired.
     * @param deadline Expired deadline of the FHERC20_EIP712_Permit.
     */
    error ERC2612ExpiredSignature(uint256 deadline);

    /**
     * @dev Mismatched signature.
     * @param signer ECDSA recovered signer of the FHERC20_EIP712_Permit.
     * @param owner Owner passed in as part of the FHERC20_EIP712_Permit struct.
     */
    error ERC2612InvalidSigner(address signer, address owner);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.25;

import {IERC20} from "@openzeppelin/contracts/token/ERC20/ERC20.sol";

interface IWETH is IERC20 {
    function withdraw(uint256 amount) external;
    function deposit() external payable;
}

{
  "evmVersion": "cancun",
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "metadata": {
    "useLiteralContent": true
  },
  "libraries": {}
}

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0000000000000000000000007b79995e5f793a07bc00c21412e50ecae098e7f9

-----Decoded View---------------
Arg [0] : wETH_ (address): 0x7b79995e5f793A07Bc00c21412e50Ecae098E7f9

-----Encoded View---------------
1 Constructor Arguments found :
Arg [0] : 0000000000000000000000007b79995e5f793a07bc00c21412e50ecae098e7f9