Contract Source Code (Solidity Standard Json-Input format)

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// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.28;

import "./EllipticCurve.sol";
import "./FastEcMul.sol";
import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "@openzeppelin/contracts/utils/cryptography/MessageHashUtils.sol";
import "@openzeppelin/contracts/utils/Strings.sol";

contract Lock {
    // use OpenZeppelin's library
    using ECDSA for bytes32;
    using MessageHashUtils for bytes32;

    // roundId -> i -> j -> share (t, w)
    mapping(string => mapping(uint => mapping(uint => uint[2]))) public shares;

    // roundId -> i -> j -> commitment (x, y)
    mapping(string => mapping(uint => mapping(uint => uint[2])))
        public commitments;

    // roundId -> j -> signature
    mapping(string => mapping(uint => bytes)) public signatures;

    // roundId -> address[]
    mapping(string => address payable[]) public IPs;
    mapping(string => address payable[]) public CPs;
    mapping(string => address payable[]) public OPs;

    // roundId -> address -> index
    mapping(string => mapping(address => uint)) public index;

    mapping(address => uint) public balance;

    // CR01: 新規マッピング
    uint256 public nextRoundId;
    mapping(string => RoundConfig) public roundConfigs;
    mapping(string => mapping(address => Endpoint)) public endpoints;
    mapping(string => mapping(address => uint)) public opRewardPaid;
    mapping(string => uint) public confirmedRewardPerOP;

    // roundId -> state
    uint public constant TIME_SPAN = 1 hours;
    mapping(string => State) public state;
    enum State {
        Preparing,
        Invoked,
        CommitmentsSubmitted,
        SignaturesSubmitted,
        SharesSubmitted,
        Terminated,
        Payout,
        Penalty
    }

    // time limit
    uint public timeLimit = 0;

    // CR01: 新規構造体
    struct PartyRequirement {
        uint minCount;
        uint maxCount;      // 0 = 無制限
        uint recruitStart;
        uint recruitEnd;
    }

    struct RoundConfig {
        string purpose;
        string dslHash;
        string dslUri;
        address payable pop;
        PartyRequirement opReq;
        PartyRequirement cpReq;
        PartyRequirement ipReq;
        uint cpRewardPerUnit;
        uint ipRewardPerUnit;
    }

    struct Endpoint {
        string spdz;
        string restApi;
    }

    struct PaymentPolicy {
        uint participationFee;
        uint resultAccessFee;  // [非推奨] 互換性のため残す
        uint ipRatio;          // [非推奨]
        uint cpRatio;          // [非推奨]
    }
    PaymentPolicy public policy;

    // CR01: イベント定義
    event RoundInitialized(
        string indexed roundId,
        address indexed pop,
        uint opMax,
        uint cpMax,
        uint ipMax
    );

    event PartyRegistered(
        string indexed roundId,
        address indexed party,
        string partyType,
        uint depositAmount
    );

    event RequirementsChecked(
        string indexed roundId,
        bool sufficient,
        uint ipCount,
        uint cpCount,
        uint opCount
    );

    event RoundStarted(
        string indexed roundId,
        uint actualRewardTotal,
        uint rewardPerOP
    );

    event RefundRecorded(
        string indexed roundId,
        address indexed op,
        uint refundAmount
    );

    event Withdrawn(address indexed party, uint amount);

    constructor() {
        policy = PaymentPolicy({
            participationFee: 0.0015 ether,
            resultAccessFee: 6 ether,  // [非推奨] 互換性のため残すが使用しない
            ipRatio: 1,                // [非推奨] 互換性のため残すが使用しない
            cpRatio: 1                 // [非推奨] 互換性のため残すが使用しない
        });
        nextRoundId = 0;
    }

    // CR01: 必須modifier
    modifier onlyPreparing(string memory roundId) {
        require(state[roundId] == State.Preparing, "Must be Preparing");
        _;
    }

    modifier onlyDeposited() {
        require(
            msg.value == policy.participationFee,
            "You need to deposit participation fee"
        );
        _;
    }
    modifier onlyPayed() {
        require(
            msg.value == policy.participationFee + policy.resultAccessFee,
            "You need to deposit participation fee and result access fee"
        );
        _;
    }

    // CR01: initializeRound
    function initializeRound(
        string memory purpose,
        string memory dslHash,
        string memory dslUri,
        uint opMin,
        uint opMax,
        uint opRecruitStart,
        uint opRecruitEnd,
        uint cpMin,
        uint cpMax,
        uint cpRewardPerUnit,
        uint cpRecruitStart,
        uint cpRecruitEnd,
        uint ipMin,
        uint ipMax,
        uint ipRewardPerUnit,
        uint ipRecruitStart,
        uint ipRecruitEnd,
        string memory spdzEndpoint,
        string memory restApiEndpoint
    ) external payable returns (string memory roundId) {
        // 検証: 最少人数
        require(opMin >= 1, "OP min count must be >= 1");
        require(cpMin >= 2, "CP min count must be >= 2");
        require(ipMin >= 2, "IP min count must be >= 2");

        // 検証: 最大人数
        require(opMax == 0 || opMax >= opMin, "OP max must be >= min or 0");
        require(cpMax >= cpMin, "CP max must be >= min");
        require(ipMax >= ipMin, "IP max must be >= min");

        // 検証: 報酬単価
        require(cpRewardPerUnit > 0, "CP reward must be > 0");
        require(ipRewardPerUnit > 0, "IP reward must be > 0");

        // 検証: 募集期間
        require(opRecruitStart < opRecruitEnd, "OP recruit period invalid");
        require(cpRecruitStart < cpRecruitEnd, "CP recruit period invalid");
        require(ipRecruitStart < ipRecruitEnd, "IP recruit period invalid");

        // 検証: msg.value
        uint rewardTotal = cpMax * cpRewardPerUnit + ipMax * ipRewardPerUnit;
        require(
            msg.value == policy.participationFee + rewardTotal,
            "Invalid deposit amount"
        );

        // roundId生成
        roundId = string(
            abi.encodePacked("round_", Strings.toString(nextRoundId++))
        );

        // RoundConfig保存
        roundConfigs[roundId] = RoundConfig({
            purpose: purpose,
            dslHash: dslHash,
            dslUri: dslUri,
            pop: payable(msg.sender),
            opReq: PartyRequirement({
                minCount: opMin,
                maxCount: opMax,
                recruitStart: opRecruitStart,
                recruitEnd: opRecruitEnd
            }),
            cpReq: PartyRequirement({
                minCount: cpMin,
                maxCount: cpMax,
                recruitStart: cpRecruitStart,
                recruitEnd: cpRecruitEnd
            }),
            ipReq: PartyRequirement({
                minCount: ipMin,
                maxCount: ipMax,
                recruitStart: ipRecruitStart,
                recruitEnd: ipRecruitEnd
            }),
            cpRewardPerUnit: cpRewardPerUnit,
            ipRewardPerUnit: ipRewardPerUnit
        });

        // POPをOPリストに追加
        OPs[roundId].push(payable(msg.sender));
        index[roundId][msg.sender] = 0;

        // エンドポイント登録
        endpoints[roundId][msg.sender] = Endpoint({
            spdz: spdzEndpoint,
            restApi: restApiEndpoint
        });

        // 報酬支払額記録
        opRewardPaid[roundId][msg.sender] = rewardTotal;

        // STATE.Preparingに遷移
        state[roundId] = State.Preparing;

        emit RoundInitialized(roundId, msg.sender, opMax, cpMax, ipMax);

        return roundId;
    }

    // CR01: registerIP (変更版)
    function registerIP(
        string memory roundId,
        string memory restApiEndpoint
    ) external payable onlyPreparing(roundId) {
        RoundConfig memory config = roundConfigs[roundId];
        require(config.pop != address(0), "Round not found");

        // 募集期間チェック
        require(
            block.timestamp >= config.ipReq.recruitStart &&
                block.timestamp <= config.ipReq.recruitEnd,
            "Outside IP recruitment period"
        );

        // 最大人数チェック
        require(
            IPs[roundId].length < config.ipReq.maxCount,
            "IP max count reached"
        );

        // msg.valueチェック
        require(
            msg.value == policy.participationFee,
            "Invalid participation fee"
        );

        IPs[roundId].push(payable(msg.sender));
        index[roundId][msg.sender] = IPs[roundId].length - 1;

        endpoints[roundId][msg.sender] = Endpoint({
            spdz: "",
            restApi: restApiEndpoint
        });

        emit PartyRegistered(
            roundId,
            msg.sender,
            "IP",
            policy.participationFee
        );
    }

    // CR01: registerCP (変更版)
    function registerCP(
        string memory roundId,
        string memory spdzEndpoint,
        string memory restApiEndpoint
    ) external payable onlyPreparing(roundId) {
        RoundConfig memory config = roundConfigs[roundId];
        require(config.pop != address(0), "Round not found");

        // 募集期間チェック
        require(
            block.timestamp >= config.cpReq.recruitStart &&
                block.timestamp <= config.cpReq.recruitEnd,
            "Outside CP recruitment period"
        );

        // 最大人数チェック
        require(
            CPs[roundId].length < config.cpReq.maxCount,
            "CP max count reached"
        );

        // msg.valueチェック
        require(
            msg.value == policy.participationFee,
            "Invalid participation fee"
        );

        CPs[roundId].push(payable(msg.sender));
        index[roundId][msg.sender] = CPs[roundId].length - 1;

        endpoints[roundId][msg.sender] = Endpoint({
            spdz: spdzEndpoint,
            restApi: restApiEndpoint
        });

        emit PartyRegistered(
            roundId,
            msg.sender,
            "CP",
            policy.participationFee
        );
    }

    // CR01: registerOP (変更版)
    function registerOP(
        string memory roundId,
        string memory spdzEndpoint,
        string memory restApiEndpoint
    ) external payable onlyPreparing(roundId) {
        RoundConfig memory config = roundConfigs[roundId];
        require(config.pop != address(0), "Round not found");

        // 募集期間チェック
        require(
            block.timestamp >= config.opReq.recruitStart &&
                block.timestamp <= config.opReq.recruitEnd,
            "Outside OP recruitment period"
        );

        // 最大人数チェック (0は無制限)
        if (config.opReq.maxCount > 0) {
            require(
                OPs[roundId].length < config.opReq.maxCount,
                "OP max count reached"
            );
        }

        // msg.valueチェック
        uint rewardTotal = config.cpReq.maxCount *
            config.cpRewardPerUnit +
            config.ipReq.maxCount *
            config.ipRewardPerUnit;
        uint requiredAmount = policy.participationFee + rewardTotal / 2;
        require(msg.value == requiredAmount, "Invalid deposit amount");

        OPs[roundId].push(payable(msg.sender));
        index[roundId][msg.sender] = OPs[roundId].length - 1;

        endpoints[roundId][msg.sender] = Endpoint({
            spdz: spdzEndpoint,
            restApi: restApiEndpoint
        });

        opRewardPaid[roundId][msg.sender] = rewardTotal / 2;

        emit PartyRegistered(roundId, msg.sender, "OP", msg.value);
    }

    // CR01: checkRequirementsAndStart
    function checkRequirementsAndStart(string memory roundId) external {
        require(state[roundId] == State.Preparing, "Must be Preparing");
        RoundConfig memory config = roundConfigs[roundId];
        require(config.pop != address(0), "Round not found");

        uint ipCount = IPs[roundId].length;
        uint cpCount = CPs[roundId].length;
        uint opCount = OPs[roundId].length;

        // 最少人数チェック
        bool sufficient = ipCount >= config.ipReq.minCount &&
            cpCount >= config.cpReq.minCount &&
            opCount >= config.opReq.minCount;

        emit RequirementsChecked(roundId, sufficient, ipCount, cpCount, opCount);

        if (!sufficient) {
            // 不足: Terminatedに遷移し、全額返金
            state[roundId] = State.Terminated;

            for (uint i = 0; i < ipCount; i++) {
                balance[IPs[roundId][i]] += policy.participationFee;
            }
            for (uint i = 0; i < cpCount; i++) {
                balance[CPs[roundId][i]] += policy.participationFee;
            }
            for (uint i = 0; i < opCount; i++) {
                address op = OPs[roundId][i];
                balance[op] += policy.participationFee + opRewardPaid[roundId][op];
            }
        } else {
            // 充足: 報酬計算とInvokedへ遷移
            uint actualRewardTotal = ipCount *
                config.ipRewardPerUnit +
                cpCount *
                config.cpRewardPerUnit;
            uint rewardPerOP = actualRewardTotal / opCount;

            confirmedRewardPerOP[roundId] = rewardPerOP;

            // OPの過剰支払い分を返却
            for (uint i = 0; i < opCount; i++) {
                address op = OPs[roundId][i];
                uint refund = opRewardPaid[roundId][op] - rewardPerOP;
                balance[op] += refund;
                emit RefundRecorded(roundId, op, refund);
            }

            state[roundId] = State.Invoked;

            emit RoundStarted(roundId, actualRewardTotal, rewardPerOP);
        }
    }

    // CR01: withdraw
    function withdraw() external {
        uint amount = balance[msg.sender];
        require(amount > 0, "No balance to withdraw");

        // Checks-Effects-Interactions
        balance[msg.sender] = 0;
        payable(msg.sender).transfer(amount);

        emit Withdrawn(msg.sender, amount);
    }

    function invoke(string memory roundId) external {
        revert("Use checkRequirementsAndStart instead");
    }

    modifier onlyInvoked(string memory roundId) {
        require(state[roundId] == State.Invoked, "State must be Invoked");
        _;
    }

    modifier postCommitmentCheck(string memory roundId) {
        _;
        for (uint i = 0; i < OPs[roundId].length; i++) {
            for (
                uint j = 0;
                j < CPs[roundId].length + OPs[roundId].length;
                j++
            ) {
                if (
                    commitments[roundId][i][j][0] == 0 &&
                    commitments[roundId][i][j][1] == 0
                ) {
                    return;
                }
            }
        }
        state[roundId] = State.CommitmentsSubmitted;
        timeLimit = block.timestamp + TIME_SPAN;
    }

    // コミットメントはそれ単体で正しさを検証する手段がないため、事前登録する形式の妥当性は要検討
    function registerCommitment(
        string memory roundId,
        uint i,
        uint j,
        uint x,
        uint y
    ) external onlyInvoked(roundId) postCommitmentCheck(roundId) {
        commitments[roundId][i][j] = [x, y];
    }

    function registerCommitments(
        string memory roundId,
        uint[] memory xs,
        uint[] memory ys
    ) external onlyInvoked(roundId) postCommitmentCheck(roundId) {
        require(xs.length == ys.length, "xs and ys must have the same length");

        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;

        for (uint i = 0; i < b; i++) {
            for (uint j = 0; j < n + b; j++) {
                // skip if the commitment is already set
                if (
                    commitments[roundId][i][j][0] != 0 ||
                    commitments[roundId][i][j][1] != 0
                ) continue;

                commitments[roundId][i][j] = [
                    xs[i * (n + b) + j],
                    ys[i * (n + b) + j]
                ];
            }
        }
    }

    modifier onlyCommitmentsSubmitted(string memory roundId) {
        require(
            state[roundId] == State.CommitmentsSubmitted,
            "State must be CommitmentsSubmitted"
        );
        _;
    }

    modifier postSignatureCheck(string memory roundId) {
        _;
        for (uint j = 0; j < CPs[roundId].length + OPs[roundId].length; j++) {
            if (signatures[roundId][j].length == 0) {
                timeLimit = block.timestamp + TIME_SPAN;
                return;
            }
        }
        state[roundId] = State.SignaturesSubmitted;
        timeLimit = block.timestamp + TIME_SPAN;
    }

    function registerSignature(
        string memory roundId,
        uint j,
        bytes memory signature
    ) external onlyCommitmentsSubmitted(roundId) postSignatureCheck(roundId) {
        // convert to EIP-191 hash
        bytes32 ethSignedMessageHash = MessageHashUtils.toEthSignedMessageHash(
            createMessageHash(roundId)
        );

        uint n = CPs[roundId].length;
        require(
            ECDSA.recover(ethSignedMessageHash, signature) ==
                (j < n ? CPs[roundId][j] : OPs[roundId][j - n]),
            "Invalid signature"
        );

        signatures[roundId][j] = signature;
    }

    function registerSignatures(
        string memory roundId,
        bytes[] memory _signatures
    ) external onlyCommitmentsSubmitted(roundId) postSignatureCheck(roundId) {
        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;
        require(_signatures.length == n + b, "Invalid number of signatures");

        for (uint j = 0; j < n + b; j++) {
            // skip if the signature is already set
            if (signatures[roundId][j].length != 0) continue;

            bytes32 ethSignedMessageHash = MessageHashUtils
                .toEthSignedMessageHash(createMessageHash(roundId));

            address target = j < n ? CPs[roundId][j] : OPs[roundId][j - n];

            if (ECDSA.recover(ethSignedMessageHash, _signatures[j]) == target) {
                signatures[roundId][j] = _signatures[j];
            } else if (msg.sender == target) {
                revert("Invalid signature");
            }
        }
    }

    modifier onlySignaturesSubmitted(string memory roundId) {
        require(
            state[roundId] == State.SignaturesSubmitted,
            "State must be SignaturesSubmitted"
        );
        _;
    }

    modifier postShareCheck(string memory roundId) {
        _;
        for (uint i = 0; i < OPs[roundId].length; i++) {
            for (
                uint j = 0;
                j < CPs[roundId].length + OPs[roundId].length;
                j++
            ) {
                if (
                    shares[roundId][i][j][0] == 0 &&
                    shares[roundId][i][j][1] == 0
                ) {
                    timeLimit = block.timestamp + TIME_SPAN;
                    return;
                }
            }
        }
        state[roundId] = State.SharesSubmitted;
    }

    function registerShare(
        string memory roundId,
        uint j,
        uint[] memory ts,
        uint[] memory ws
    ) external onlySignaturesSubmitted(roundId) postShareCheck(roundId) {
        uint b = OPs[roundId].length;
        for (uint i = 0; i < b; i++) {
            (uint x, uint y) = LockLib.createPedersenCommitment(ts[i], ws[i]);

            require(
                x == commitments[roundId][i][j][0] &&
                    y == commitments[roundId][i][j][1],
                "Invalid share"
            );

            shares[roundId][i][j] = [ts[i], ws[i]];
        }
    }

    function registerShares(
        string memory roundId,
        uint[] memory ts,
        uint[] memory ws
    ) external onlySignaturesSubmitted(roundId) postShareCheck(roundId) {
        require(ts.length == ws.length, "ts and ws must have the same length");

        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;

        for (uint i = 0; i < b; i++) {
            for (uint j = 0; j < n + b; j++) {
                // skip if the share is already set
                if (
                    shares[roundId][i][j][0] != 0 &&
                    shares[roundId][i][j][1] != 0
                ) continue;

                (uint x, uint y) = LockLib.createPedersenCommitment(
                    ts[i * (n + b) + j],
                    ws[i * (n + b) + j]
                );

                address target = j < n ? CPs[roundId][j] : OPs[roundId][j - n];

                if (
                    x == commitments[roundId][i][j][0] &&
                    y == commitments[roundId][i][j][1]
                ) {
                    shares[roundId][i][j] = [
                        ts[i * (n + b) + j],
                        ws[i * (n + b) + j]
                    ];
                } else if (msg.sender == target) {
                    revert("Invalid share");
                }
            }
        }
    }

    function exit(string memory roundId) external {
        State s = state[roundId];

        require(
            s != State.Payout && s != State.Penalty && s != State.Terminated,
            "State must not be Ready, Payout, Penalty, or Terminated"
        );

        if (s == State.Preparing || s == State.Invoked) {
            state[roundId] = State.Terminated;
            returnDeposit(roundId);
        } else if (
            s == State.CommitmentsSubmitted && block.timestamp > timeLimit
        ) {
            state[roundId] = State.Penalty;
            signaturePenalty(roundId);
        } else if (
            s == State.SignaturesSubmitted && block.timestamp > timeLimit
        ) {
            state[roundId] = State.Penalty;
            sharePenalty(roundId);
        } else if (s == State.SharesSubmitted) {
            state[roundId] = State.Payout;
            payout(roundId);
        } else {
            revert("Time limit has not passed");
        }
    }

    // CR01: returnDeposit (変更版)
    function returnDeposit(string memory roundId) private {
        for (uint i = 0; i < IPs[roundId].length; i++) {
            balance[IPs[roundId][i]] += policy.participationFee;
        }
        for (uint i = 0; i < CPs[roundId].length; i++) {
            balance[CPs[roundId][i]] += policy.participationFee;
        }
        for (uint i = 0; i < OPs[roundId].length; i++) {
            address op = OPs[roundId][i];
            // STATE.Preparing時: opRewardPaidを使用（checkRequirementsAndStart未実行）
            // STATE.Invoked時: confirmedRewardPerOPを使用（過剰分は既に返却済み）
            uint opReward = state[roundId] == State.Preparing
                ? opRewardPaid[roundId][op]
                : confirmedRewardPerOP[roundId];
            balance[op] += policy.participationFee + opReward;
        }
    }

    // CR01: signaturePenalty (変更版)
    function signaturePenalty(string memory roundId) private {
        uint a = IPs[roundId].length;
        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;

        uint m = 0;
        for (uint j = 0; j < n + b; j++) {
            if (signatures[roundId][j].length != 0) {
                address target = j < n ? CPs[roundId][j] : OPs[roundId][j - n];
                balance[target] += policy.participationFee;
            } else {
                m++;
                if (j >= n)
                    balance[OPs[roundId][j - n]] += confirmedRewardPerOP[
                        roundId
                    ];
            }
        }

        uint payback = (policy.participationFee * m) / (a + n + b - m);
        for (uint i = 0; i < a; i++) balance[IPs[roundId][i]] += payback;
        for (uint j = 0; j < n + b; j++) {
            if (signatures[roundId][j].length != 0) {
                address target = j < n ? CPs[roundId][j] : OPs[roundId][j - n];
                balance[target] += payback;
            }
        }
    }

    // CR01: sharePenalty (変更版)
    function sharePenalty(string memory roundId) private {
        uint a = IPs[roundId].length;
        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;

        uint m = 0;
        for (uint i = 0; i < b; i++) {
            for (uint j = 0; j < n + b; j++) {
                if (
                    shares[roundId][i][j][0] != 0 &&
                    shares[roundId][i][j][1] != 0
                ) {
                    address target = j < n
                        ? CPs[roundId][j]
                        : OPs[roundId][j - n];
                    balance[target] += policy.participationFee;
                } else {
                    m++;
                    if (j >= n)
                        balance[OPs[roundId][j - n]] += confirmedRewardPerOP[
                            roundId
                        ];
                }
            }
        }

        uint payback = (policy.participationFee * m) / (a + n + b - m);
        for (uint i = 0; i < a; i++) balance[IPs[roundId][i]] += payback;
        for (uint i = 0; i < b; i++) {
            for (uint j = 0; j < n + b; j++) {
                if (
                    shares[roundId][i][j][0] != 0 &&
                    shares[roundId][i][j][1] != 0
                ) {
                    address target = j < n
                        ? CPs[roundId][j]
                        : OPs[roundId][j - n];
                    balance[target] += payback;
                }
            }
        }
    }

    // CR01: payout (変更版)
    function payout(string memory roundId) private {
        RoundConfig memory config = roundConfigs[roundId];

        uint ipCount = IPs[roundId].length;
        uint cpCount = CPs[roundId].length;
        uint opCount = OPs[roundId].length;

        uint cpRewardPerUnit = config.cpRewardPerUnit;
        uint ipRewardPerUnit = config.ipRewardPerUnit;

        // IP報酬支払い
        for (uint i = 0; i < ipCount; i++) {
            balance[IPs[roundId][i]] +=
                policy.participationFee +
                ipRewardPerUnit;
        }

        // CP報酬支払い
        for (uint i = 0; i < cpCount; i++) {
            balance[CPs[roundId][i]] +=
                policy.participationFee +
                cpRewardPerUnit;
        }

        // OP参加費返却
        for (uint i = 0; i < opCount; i++) {
            balance[OPs[roundId][i]] += policy.participationFee;
        }
    }

    function createMessageHash(
        string memory roundId
    ) public view onlyCommitmentsSubmitted(roundId) returns (bytes32) {
        uint n = CPs[roundId].length;
        uint b = OPs[roundId].length;

        uint[] memory flattened = new uint[](b * (n + b) * 2);
        for (uint i = 0; i < b; i++) {
            for (uint j = 0; j < n + b; j++) {
                for (uint k = 0; k < 2; k++) {
                    flattened[i * (n + b) * 2 + j * 2 + k] = commitments[
                        roundId
                    ][i][j][k];
                }
            }
        }
        bytes32 messageHash = keccak256(abi.encode(flattened));
        return messageHash;
    }
}

library LockLib {
    // define parameters of elliptic curve as constants
    uint private constant N =
        115792089237316195423570985008687907852837564279074904382605163141518161494337;
    uint private constant P =
        115792089237316195423570985008687907853269984665640564039457584007908834671663;
    uint private constant Gx =
        55066263022277343669578718895168534326250603453777594175500187360389116729240;
    uint private constant Gy =
        32670510020758816978083085130507043184471273380659243275938904335757337482424;
    uint private constant Hx =
        19678015404333929029128013708488027270870144796102827091528430274610966132548;
    uint private constant Hy =
        7750785029508853713910290324108018932599102225606536719127495477978726181969;

    function createPedersenCommitment(
        uint u,
        uint r
    ) external pure returns (uint, uint) {
        (uint uGx, uint uGy) = EllipticCurve.ecMul(u, Gx, Gy, 0, P);
        (uint rHx, uint rHy) = EllipticCurve.ecMul(r, Hx, Hy, 0, P);
        (uint cx, uint cy) = EllipticCurve.ecAdd(uGx, uGy, rHx, rHy, 0, P);

        return (cx, cy);
    }
}

// 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/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 v5.3.0) (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 v5.1.0) (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 v5.4.0) (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(add(buffer, 0x20), 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(add(buffer, 0x20), offset))
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 ** @title Elliptic Curve Library
 ** @dev Library providing arithmetic operations over elliptic curves.
 ** This library does not check whether the inserted points belong to the curve
 ** `isOnCurve` function should be used by the library user to check the aforementioned statement.
 ** @author Witnet Foundation
 */
library EllipticCurve {
    // Pre-computed constant for 2 ** 255
    uint256 private constant U255_MAX_PLUS_1 =
        57896044618658097711785492504343953926634992332820282019728792003956564819968;

    /// @dev Modular euclidean inverse of a number (mod p).
    /// @param _x The number
    /// @param _pp The modulus
    /// @return q such that x*q = 1 (mod _pp)
    function invMod(uint256 _x, uint256 _pp) internal pure returns (uint256) {
        require(_x != 0 && _x != _pp && _pp != 0, "Invalid number");
        uint256 q = 0;
        uint256 newT = 1;
        uint256 r = _pp;
        uint256 t;
        while (_x != 0) {
            t = r / _x;
            (q, newT) = (newT, addmod(q, (_pp - mulmod(t, newT, _pp)), _pp));
            (r, _x) = (_x, r - t * _x);
        }

        return q;
    }

    /// @dev Modular exponentiation, b^e % _pp.
    /// Source: https://github.com/androlo/standard-contracts/blob/master/contracts/src/crypto/ECCMath.sol
    /// @param _base base
    /// @param _exp exponent
    /// @param _pp modulus
    /// @return r such that r = b**e (mod _pp)
    function expMod(
            uint256 _base,
            uint256 _exp,
            uint256 _pp
        )
        internal pure
        returns (uint256) 
    {
        require(_pp != 0, "EllipticCurve: modulus is zero");

        if (_base == 0) return 0;
        if (_exp == 0) return 1;

        uint256 r = 1;
        uint256 bit = U255_MAX_PLUS_1;
        assembly {
            for {

            } gt(bit, 0) {

            } {
                r := mulmod(
                    mulmod(r, r, _pp),
                    exp(_base, iszero(iszero(and(_exp, bit)))),
                    _pp
                )
                r := mulmod(
                    mulmod(r, r, _pp),
                    exp(_base, iszero(iszero(and(_exp, div(bit, 2))))),
                    _pp
                )
                r := mulmod(
                    mulmod(r, r, _pp),
                    exp(_base, iszero(iszero(and(_exp, div(bit, 4))))),
                    _pp
                )
                r := mulmod(
                    mulmod(r, r, _pp),
                    exp(_base, iszero(iszero(and(_exp, div(bit, 8))))),
                    _pp
                )
                bit := div(bit, 16)
            }
        }

        return r;
    }

    /// @dev Converts a point (x, y, z) expressed in Jacobian coordinates to affine coordinates (x', y', 1).
    /// @param _x coordinate x
    /// @param _y coordinate y
    /// @param _z coordinate z
    /// @param _pp the modulus
    /// @return (x', y') affine coordinates
    function toAffine(
            uint256 _x,
            uint256 _y,
            uint256 _z,
            uint256 _pp
        )
        internal pure 
        returns (uint256, uint256) 
    {
        uint256 zInv = invMod(_z, _pp);
        uint256 zInv2 = mulmod(zInv, zInv, _pp);
        uint256 x2 = mulmod(_x, zInv2, _pp);
        uint256 y2 = mulmod(_y, mulmod(zInv, zInv2, _pp), _pp);

        return (x2, y2);
    }

    /// @dev Derives the y coordinate from a compressed-format point x [[SEC-1]](https://www.secg.org/SEC1-Ver-1.0.pdf).
    /// @param _prefix parity byte (0x02 even, 0x03 odd)
    /// @param _x coordinate x
    /// @param _aa constant of curve
    /// @param _bb constant of curve
    /// @param _pp the modulus
    /// @return y coordinate y
    function deriveY(
            uint8 _prefix,
            uint256 _x,
            uint256 _aa,
            uint256 _bb,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256) 
    {
        require(
            _prefix == 0x02 || _prefix == 0x03,
            "EllipticCurve:innvalid compressed EC point prefix"
        );

        // x^3 + ax + b
        uint256 y2 = addmod(
            mulmod(_x, mulmod(_x, _x, _pp), _pp),
            addmod(mulmod(_x, _aa, _pp), _bb, _pp),
            _pp
        );
        y2 = expMod(y2, (_pp + 1) / 4, _pp);
        // uint256 cmp = yBit ^ y_ & 1;
        uint256 y = (y2 + _prefix) % 2 == 0 ? y2 : _pp - y2;

        return y;
    }

    /// @dev Check whether point (x,y) is on curve defined by a, b, and _pp.
    /// @param _x coordinate x of P1
    /// @param _y coordinate y of P1
    /// @param _aa constant of curve
    /// @param _bb constant of curve
    /// @param _pp the modulus
    /// @return true if x,y in the curve, false else
    function isOnCurve(
            uint _x,
            uint _y,
            uint _aa,
            uint _bb,
            uint _pp
        ) 
        internal pure 
        returns (bool) 
    {
        if (0 == _x || _x >= _pp || 0 == _y || _y >= _pp) {
            return false;
        }
        // y^2
        uint lhs = mulmod(_y, _y, _pp);
        // x^3
        uint rhs = mulmod(mulmod(_x, _x, _pp), _x, _pp);
        if (_aa != 0) {
            // x^3 + a*x
            rhs = addmod(rhs, mulmod(_x, _aa, _pp), _pp);
        }
        if (_bb != 0) {
            // x^3 + a*x + b
            rhs = addmod(rhs, _bb, _pp);
        }

        return lhs == rhs;
    }

    /// @dev Calculate inverse (x, -y) of point (x, y).
    /// @param _x coordinate x of P1
    /// @param _y coordinate y of P1
    /// @param _pp the modulus
    /// @return (x, -y)
    function ecInv(
            uint256 _x,
            uint256 _y,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256) 
    {
        return (_x, (_pp - _y) % _pp);
    }

    /// @dev Add two points (x1, y1) and (x2, y2) in affine coordinates.
    /// @param _x1 coordinate x of P1
    /// @param _y1 coordinate y of P1
    /// @param _x2 coordinate x of P2
    /// @param _y2 coordinate y of P2
    /// @param _aa constant of the curve
    /// @param _pp the modulus
    /// @return (qx, qy) = P1+P2 in affine coordinates
    function ecAdd(
            uint256 _x1,
            uint256 _y1,
            uint256 _x2,
            uint256 _y2,
            uint256 _aa,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256) 
    {
        uint x = 0;
        uint y = 0;
        uint z = 0;

        // Double if x1==x2 else add
        if (_x1 == _x2) {
            // y1 = -y2 mod p
            if (addmod(_y1, _y2, _pp) == 0) {
                return (0, 0);
            } else {
                // P1 = P2
                (x, y, z) = jacDouble(_x1, _y1, 1, _aa, _pp);
            }
        } else {
            (x, y, z) = jacAdd(_x1, _y1, 1, _x2, _y2, 1, _pp);
        }
        // Get back to affine
        return toAffine(x, y, z, _pp);
    }

    /// @dev Substract two points (x1, y1) and (x2, y2) in affine coordinates.
    /// @param _x1 coordinate x of P1
    /// @param _y1 coordinate y of P1
    /// @param _x2 coordinate x of P2
    /// @param _y2 coordinate y of P2
    /// @param _aa constant of the curve
    /// @param _pp the modulus
    /// @return (qx, qy) = P1-P2 in affine coordinates
    function ecSub(
            uint256 _x1,
            uint256 _y1,
            uint256 _x2,
            uint256 _y2,
            uint256 _aa,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256) 
    {
        // invert square
        (uint256 x, uint256 y) = ecInv(_x2, _y2, _pp);
        // P1-square
        return ecAdd(_x1, _y1, x, y, _aa, _pp);
    }

    /// @dev Multiply point (x1, y1, z1) times d in affine coordinates.
    /// @param _k scalar to multiply
    /// @param _x coordinate x of P1
    /// @param _y coordinate y of P1
    /// @param _aa constant of the curve
    /// @param _pp the modulus
    /// @return (qx, qy) = d*P in affine coordinates
    function ecMul(
            uint256 _k,
            uint256 _x,
            uint256 _y,
            uint256 _aa,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256) 
    {
        // Jacobian multiplication
        (uint256 x1, uint256 y1, uint256 z1) = jacMul(_k, _x, _y, 1, _aa, _pp);
        // Get back to affine
        return toAffine(x1, y1, z1, _pp);
    }

    /// @dev Adds two points (x1, y1, z1) and (x2 y2, z2).
    /// @param _x1 coordinate x of P1
    /// @param _y1 coordinate y of P1
    /// @param _z1 coordinate z of P1
    /// @param _x2 coordinate x of square
    /// @param _y2 coordinate y of square
    /// @param _z2 coordinate z of square
    /// @param _pp the modulus
    /// @return (qx, qy, qz) P1+square in Jacobian
    function jacAdd(
            uint256 _x1,
            uint256 _y1,
            uint256 _z1,
            uint256 _x2,
            uint256 _y2,
            uint256 _z2,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256, uint256) 
    {
        if (_x1 == 0 && _y1 == 0) return (_x2, _y2, _z2);
        if (_x2 == 0 && _y2 == 0) return (_x1, _y1, _z1);

        // We follow the equations described in https://pdfs.semanticscholar.org/5c64/29952e08025a9649c2b0ba32518e9a7fb5c2.pdf Section 5
        uint[4] memory zs; // z1^2, z1^3, z2^2, z2^3
        zs[0] = mulmod(_z1, _z1, _pp);
        zs[1] = mulmod(_z1, zs[0], _pp);
        zs[2] = mulmod(_z2, _z2, _pp);
        zs[3] = mulmod(_z2, zs[2], _pp);

        // u1, s1, u2, s2
        zs = [
            mulmod(_x1, zs[2], _pp),
            mulmod(_y1, zs[3], _pp),
            mulmod(_x2, zs[0], _pp),
            mulmod(_y2, zs[1], _pp)
        ];

        // In case of zs[0] == zs[2] && zs[1] == zs[3], double function should be used
        require(
            zs[0] != zs[2] || zs[1] != zs[3],
            "Use jacDouble function instead"
        );

        uint[4] memory hr;
        //h
        hr[0] = addmod(zs[2], _pp - zs[0], _pp);
        //r
        hr[1] = addmod(zs[3], _pp - zs[1], _pp);
        //h^2
        hr[2] = mulmod(hr[0], hr[0], _pp);
        // h^3
        hr[3] = mulmod(hr[2], hr[0], _pp);
        // qx = -h^3  -2u1h^2+r^2
        uint256 qx = addmod(mulmod(hr[1], hr[1], _pp), _pp - hr[3], _pp);
        qx = addmod(qx, _pp - mulmod(2, mulmod(zs[0], hr[2], _pp), _pp), _pp);
        // qy = -s1*z1*h^3+r(u1*h^2 -x^3)
        uint256 qy = mulmod(
            hr[1],
            addmod(mulmod(zs[0], hr[2], _pp), _pp - qx, _pp),
            _pp
        );
        qy = addmod(qy, _pp - mulmod(zs[1], hr[3], _pp), _pp);
        // qz = h*z1*z2
        uint256 qz = mulmod(hr[0], mulmod(_z1, _z2, _pp), _pp);
        return (qx, qy, qz);
    }

    /// @dev Doubles a points (x, y, z).
    /// @param _x coordinate x of P1
    /// @param _y coordinate y of P1
    /// @param _z coordinate z of P1
    /// @param _aa the a scalar in the curve equation
    /// @param _pp the modulus
    /// @return (qx, qy, qz) 2P in Jacobian
    function jacDouble(
            uint256 _x,
            uint256 _y,
            uint256 _z,
            uint256 _aa,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256, uint256) 
    {
        if (_z == 0) return (_x, _y, _z);

        // We follow the equations described in https://pdfs.semanticscholar.org/5c64/29952e08025a9649c2b0ba32518e9a7fb5c2.pdf Section 5
        // Note: there is a bug in the paper regarding the m parameter, M=3*(x1^2)+a*(z1^4)
        // x, y, z at this point represent the squares of _x, _y, _z
        uint256 x = mulmod(_x, _x, _pp); //x1^2
        uint256 y = mulmod(_y, _y, _pp); //y1^2
        uint256 z = mulmod(_z, _z, _pp); //z1^2

        // s
        uint s = mulmod(4, mulmod(_x, y, _pp), _pp);
        // m
        uint m = addmod(
            mulmod(3, x, _pp),
            mulmod(_aa, mulmod(z, z, _pp), _pp),
            _pp
        );

        // x, y, z at this point will be reassigned and rather represent qx, qy, qz from the paper
        // This allows to reduce the gas cost and stack footprint of the algorithm
        // qx
        x = addmod(mulmod(m, m, _pp), _pp - addmod(s, s, _pp), _pp);
        // qy = -8*y1^4 + M(S-T)
        y = addmod(
            mulmod(m, addmod(s, _pp - x, _pp), _pp),
            _pp - mulmod(8, mulmod(y, y, _pp), _pp),
            _pp
        );
        // qz = 2*y1*z1
        z = mulmod(2, mulmod(_y, _z, _pp), _pp);

        return (x, y, z);
    }

    /// @dev Multiply point (x, y, z) times d.
    /// @param _d scalar to multiply
    /// @param _x coordinate x of P1
    /// @param _y coordinate y of P1
    /// @param _z coordinate z of P1
    /// @param _aa constant of curve
    /// @param _pp the modulus
    /// @return (qx, qy, qz) d*P1 in Jacobian
    function jacMul(
            uint256 _d,
            uint256 _x,
            uint256 _y,
            uint256 _z,
            uint256 _aa,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256, uint256) 
    {
        // Early return in case that `_d == 0`
        if (_d == 0) {
            return (_x, _y, _z);
        }

        uint256 remaining = _d;
        uint256 qx = 0;
        uint256 qy = 0;
        uint256 qz = 1;

        // Double and add algorithm
        while (remaining != 0) {
            if ((remaining & 1) != 0) {
                (qx, qy, qz) = jacAdd(qx, qy, qz, _x, _y, _z, _pp);
            }
            remaining = remaining / 2;
            (_x, _y, _z) = jacDouble(_x, _y, _z, _aa, _pp);
        }
        return (qx, qy, qz);
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./EllipticCurve.sol";

/**
 ** @title Fast Elliptic Curve Multiplication Library
 ** @dev Library providing the following speed ups to an elliptic curve multiplication operation.
 **      - wNAF scalar representation
 **      - scalar decomposition through endomorphism
 ** This library does not check whether the inserted points belong to the curve
 ** `isOnCurve` function should be used by the library user to check the aforementioned statement.
 ** @author Witnet Foundation
 **/
library FastEcMul {
    // Pre-computed constant for 2 ** 128 - 1
    uint256 private constant U128_MAX = 340282366920938463463374607431768211455;

    /// @dev Decomposition of the scalar k in two scalars k1 and k2 with half bit-length, such that k=k1+k2*LAMBDA (mod n)
    /// @param _k the scalar to be decompose
    /// @param _nn the modulus
    /// @param _lambda is a root of the characteristic polynomial of an endomorphism of the curve
    /// @return k1 and k2  such that k=k1+k2*LAMBDA (mod n)
    function decomposeScalar(
            uint256 _k,
            uint256 _nn,
            uint256 _lambda
        ) 
        internal pure 
        returns (int256, int256) 
    {
        uint256 k = _k % _nn;
        // Extended Euclidean Algorithm for n and LAMBDA
        int256[2] memory t;
        t[0] = 1;
        t[1] = 0;
        uint256[2] memory r;
        r[0] = uint256(_lambda);
        r[1] = uint256(_nn);

        // Loop while `r[0] >= sqrt(_nn)`
        // Or in other words, `r[0] * r[0] >= _nn`
        // When `r[0] >= 2**128`, `r[0] * r[0]` will overflow so we must check that before
        while ((r[0] >= 2 ** 128) || (r[0] * r[0] >= _nn)) {
            uint256 quotient = r[1] / r[0];
            (r[1], r[0]) = (r[0], r[1] - quotient * r[0]);
            (t[1], t[0]) = (t[0], t[1] - int256(quotient) * t[0]);
        }
        int256[4] memory ab;

        // the vectors v1=(a1, b1) and v2=(a2,b2)
        ab[0] = int256(r[0]);
        ab[1] = int256(-t[0]);
        ab[2] = int256(r[1]);
        ab[3] = int256(-t[1]);

        //b2*K
        uint[3] memory test;
        (test[0], test[1], test[2]) = _multiply256(uint(ab[3]), uint(k));

        //-b1*k
        uint[3] memory test2;
        (test2[0], test2[1], test2[2]) = _multiply256(uint(-ab[1]), uint(k));

        //c1 and c2
        uint[2] memory c1;
        (c1[0], c1[1]) = _bigDivision(
            (uint256(uint128(test[0])) << 128) | uint128(test[1]),
            uint256(test[2]) + (_nn / 2),
            _nn
        );
        uint[2] memory c2;
        (c2[0], c2[1]) = _bigDivision(
            (uint256(uint128(test2[0])) << 128) | uint128(test2[1]),
            uint256(test2[2]) + (_nn / 2),
            _nn
        );

        // the decomposition of k in k1 and k2
        int256 k1 = int256(
            (int256(k) -
                int256(c1[0]) *
                int256(ab[0]) -
                int256(c2[0]) *
                int256(ab[2])) % int256(_nn)
        );
        int256 k2 = int256(
            (-int256(c1[0]) * int256(ab[1]) - int256(c2[0]) * int256(ab[3])) %
                int256(_nn)
        );
        if (uint256(_abs(k1)) > (_nn / 2)) {
            k1 = int256(uint256(k1) - _nn);
        }
        if (uint256(_abs(k2)) > (_nn / 2)) {
            k2 = int256(uint256(k2) - _nn);
        }

        return (k1, k2);
    }

    /// @notice Simultaneous multiplication of the form kP + lQ.
    /// @dev Scalars k and l are expected to be decomposed such that k = k1 + k2 λ, and l = l1 + l2 λ,
    /// where λ is specific to the endomorphism of the curve.
    /// @param _scalars An array with the decomposition of k and l values, i.e., [k1, k2, l1, l2]
    /// @param _points An array with the affine coordinates of both P and Q, i.e., [P1, P2, Q1, Q2]
    function ecSimMul(
            int256[4] memory _scalars,
            uint256[4] memory _points,
            uint256 _aa,
            uint256 _beta,
            uint256 _pp
        ) 
        internal pure 
        returns (uint256, uint256) 
    {
        uint256[4] memory wnaf;
        uint256 maxCount = 0;
        uint256 count = 0;

        for (uint j = 0; j < 4; j++) {
            (wnaf[j], count) = _wnaf(_scalars[j]);
            if (count > maxCount) {
                maxCount = count;
            }
        }

        (uint256 x, uint256 y, uint256 z) = _simMulWnaf(
            wnaf,
            maxCount,
            _points,
            _aa,
            _beta,
            _pp
        );

        return EllipticCurve.toAffine(x, y, z, _pp);
    }

    /// @dev Compute the look up table for the simultaneous multiplication (P, 3P,..,Q,3Q,..).
    /// @param _iP the look up table were values will be stored
    /// @param _points the points P and Q to be multiplied
    /// @param _aa constant of the curve
    /// @param _beta constant of the curve (endomorphism)
    /// @param _pp the modulus
    function _lookupSimMul(
            uint256[3][4][4] memory _iP,
            uint256[4] memory _points,
            uint256 _aa,
            uint256 _beta,
            uint256 _pp
        ) 
        private pure 
    {
        uint256[3][4] memory iPj;
        uint256[3] memory double;

        // P1 Lookup Table
        iPj = _iP[0];
        iPj[0] = [_points[0], _points[1], 1]; // P1

        (double[0], double[1], double[2]) = EllipticCurve.jacDouble(
            iPj[0][0],
            iPj[0][1],
            1,
            _aa,
            _pp
        );
        (iPj[1][0], iPj[1][1], iPj[1][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[0][0],
            iPj[0][1],
            iPj[0][2],
            _pp
        );
        (iPj[2][0], iPj[2][1], iPj[2][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[1][0],
            iPj[1][1],
            iPj[1][2],
            _pp
        );
        (iPj[3][0], iPj[3][1], iPj[3][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[2][0],
            iPj[2][1],
            iPj[2][2],
            _pp
        );

        // P2 Lookup Table
        _iP[1][0] = [mulmod(_beta, _points[0], _pp), _points[1], 1]; // P2

        _iP[1][1] = [mulmod(_beta, iPj[1][0], _pp), iPj[1][1], iPj[1][2]];
        _iP[1][2] = [mulmod(_beta, iPj[2][0], _pp), iPj[2][1], iPj[2][2]];
        _iP[1][3] = [mulmod(_beta, iPj[3][0], _pp), iPj[3][1], iPj[3][2]];

        // Q1 Lookup Table
        iPj = _iP[2];
        iPj[0] = [_points[2], _points[3], 1]; // Q1
        (double[0], double[1], double[2]) = EllipticCurve.jacDouble(
            iPj[0][0],
            iPj[0][1],
            1,
            _aa,
            _pp
        );
        (iPj[1][0], iPj[1][1], iPj[1][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[0][0],
            iPj[0][1],
            iPj[0][2],
            _pp
        );
        (iPj[2][0], iPj[2][1], iPj[2][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[1][0],
            iPj[1][1],
            iPj[1][2],
            _pp
        );
        (iPj[3][0], iPj[3][1], iPj[3][2]) = EllipticCurve.jacAdd(
            double[0],
            double[1],
            double[2],
            iPj[2][0],
            iPj[2][1],
            iPj[2][2],
            _pp
        );

        // Q2 Lookup Table
        _iP[3][0] = [mulmod(_beta, _points[2], _pp), _points[3], 1]; // P2

        _iP[3][1] = [mulmod(_beta, iPj[1][0], _pp), iPj[1][1], iPj[1][2]];
        _iP[3][2] = [mulmod(_beta, iPj[2][0], _pp), iPj[2][1], iPj[2][2]];
        _iP[3][3] = [mulmod(_beta, iPj[3][0], _pp), iPj[3][1], iPj[3][2]];
    }

    /// @dev WNAF integer representation. Computes the WNAF representation of an integer, and puts the resulting array of coefficients in memory.
    /// @param _k A 256-bit integer
    /// @return (ptr, length) The pointer to the first coefficient, and the total length of the array
    function _wnaf(int256 _k) private pure returns (uint256, uint256) {
        int sign = _k < 0 ? -1 : int(1);
        uint256 k = uint256(sign * _k);

        uint256 ptr;
        uint256 length = 0;
        assembly {
            let ki := 0
            ptr := mload(0x40) // Get free memory pointer
            mstore(0x40, add(ptr, 300)) // Updates free memory pointer to +300 bytes offset
            for {

            } gt(k, 0) {

            } {
                // while k > 0
                if and(k, 1) {
                    // if k is odd:
                    ki := mod(k, 16)
                    k := add(sub(k, ki), mul(gt(ki, 8), 16))
                    // if sign = 1, store ki; if sign = -1, store 16 - ki
                    mstore8(
                        add(ptr, length),
                        add(mul(ki, sign), sub(8, mul(sign, 8)))
                    )
                }
                length := add(length, 1)
                k := div(k, 2)
            }
        }

        return (ptr, length);
    }

    /// @dev Compute the simultaneous multiplication with wnaf decomposed scalar.
    /// @param _wnafPointer the decomposed scalars to be multiplied in wnaf form (k1, k2, l1, l2)
    /// @param  _length the length of the WNAF representation array
    /// @param _points the points P and Q to be multiplied
    /// @param _aa constant of the curve
    /// @param _beta constant of the curve (endomorphism)
    /// @param _pp the modulus
    /// @return (qx, qy, qz) d*P1 in Jacobian
    function _simMulWnaf(
            uint256[4] memory _wnafPointer,
            uint256 _length,
            uint256[4] memory _points,
            uint256 _aa,
            uint256 _beta,
            uint256 _pp
        ) 
        private pure 
        returns (uint256, uint256, uint256) 
    {
        uint[3] memory mulPoint;
        uint256[3][4][4] memory iP;
        _lookupSimMul(iP, _points, _aa, _beta, _pp);

        uint256 ki;
        uint256 ptr;
        while (_length > 0) {
            _length--;

            (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacDouble(
                mulPoint[0],
                mulPoint[1],
                mulPoint[2],
                _aa,
                _pp
            );

            ptr = _wnafPointer[0] + _length;
            assembly {
                ki := byte(0, mload(ptr))
            }

            if (ki > 8) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[0][(15 - ki) / 2][0],
                    (_pp - iP[0][(15 - ki) / 2][1]) % _pp,
                    iP[0][(15 - ki) / 2][2],
                    _pp
                );
            } else if (ki > 0) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[0][(ki - 1) / 2][0],
                    iP[0][(ki - 1) / 2][1],
                    iP[0][(ki - 1) / 2][2],
                    _pp
                );
            }

            ptr = _wnafPointer[1] + _length;
            assembly {
                ki := byte(0, mload(ptr))
            }

            if (ki > 8) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[1][(15 - ki) / 2][0],
                    (_pp - iP[1][(15 - ki) / 2][1]) % _pp,
                    iP[1][(15 - ki) / 2][2],
                    _pp
                );
            } else if (ki > 0) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[1][(ki - 1) / 2][0],
                    iP[1][(ki - 1) / 2][1],
                    iP[1][(ki - 1) / 2][2],
                    _pp
                );
            }

            ptr = _wnafPointer[2] + _length;
            assembly {
                ki := byte(0, mload(ptr))
            }

            if (ki > 8) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[2][(15 - ki) / 2][0],
                    (_pp - iP[2][(15 - ki) / 2][1]) % _pp,
                    iP[2][(15 - ki) / 2][2],
                    _pp
                );
            } else if (ki > 0) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[2][(ki - 1) / 2][0],
                    iP[2][(ki - 1) / 2][1],
                    iP[2][(ki - 1) / 2][2],
                    _pp
                );
            }

            ptr = _wnafPointer[3] + _length;
            assembly {
                ki := byte(0, mload(ptr))
            }

            if (ki > 8) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[3][(15 - ki) / 2][0],
                    (_pp - iP[3][(15 - ki) / 2][1]) % _pp,
                    iP[3][(15 - ki) / 2][2],
                    _pp
                );
            } else if (ki > 0) {
                (mulPoint[0], mulPoint[1], mulPoint[2]) = EllipticCurve.jacAdd(
                    mulPoint[0],
                    mulPoint[1],
                    mulPoint[2],
                    iP[3][(ki - 1) / 2][0],
                    iP[3][(ki - 1) / 2][1],
                    iP[3][(ki - 1) / 2][2],
                    _pp
                );
            }
        }

        return (mulPoint[0], mulPoint[1], mulPoint[2]);
    }

    /// @dev Multiplication of a uint256 a and uint256 b. Because in Solidity each variable can not be greater than 256 bits,
    /// this function separates the result of the multiplication in three parts, so the result would be the concatenation of those three.
    /// @param _a uint256
    /// @param _b uint256
    /// @return (ab2, ab1, ab0)
    function _multiply256(
            uint256 _a,
            uint256 _b
        ) 
        private pure 
        returns (uint256, uint256, uint256) 
    {
        uint256 aM = _a >> 128;
        uint256 am = _a & U128_MAX;
        uint256 bM = _b >> 128;
        uint256 bm = _b & U128_MAX;
        uint256 ab0 = am * bm;
        uint256 ab1 = (ab0 >> 128) +
            ((aM * bm) & U128_MAX) +
            ((am * bM) & U128_MAX);
        uint256 ab2 = (ab1 >> 128) +
            aM *
            bM +
            ((aM * bm) >> 128) +
            ((am * bM) >> 128);
        ab1 &= U128_MAX;
        ab0 &= U128_MAX;

        return (ab2, ab1, ab0);
    }

    /// @dev Division of an integer of 312 bits by a 256-bit integer.
    /// @param _aM the higher 256 bits of the numarator
    /// @param _am the lower 128 bits of the numarator
    /// @param _b the 256-bit denominator
    /// @return q the result of the division and the rest r
    function _bigDivision(
            uint256 _aM,
            uint256 _am,
            uint256 _b
        ) 
        private pure 
        returns (uint256, uint256) 
    {
        uint256 aM = _aM % _b;

        uint256 shift = 0;
        while (_b >> shift > 0) {
            shift++;
        }
        shift = 256 - shift;
        aM =
            (_aM << shift) +
            (shift > 128 ? _am << (shift - 128) : _am >> (128 - shift));
        uint256 a0 = (_am << shift) & U128_MAX;

        (uint256 b1, uint256 b0) = (
            (_b << shift) >> 128,
            (_b << shift) & U128_MAX
        );

        uint256 rM;
        uint256 q = aM / b1;
        rM = aM % b1;

        uint256 rsub0 = (q & U128_MAX) * b0;
        uint256 rsub21 = (q >> 128) * b0 + (rsub0 >> 128);
        rsub0 &= U128_MAX;

        while (rsub21 > rM || (rsub21 == rM && rsub0 > a0)) {
            q--;
            a0 += b0;
            rM += b1 + (a0 >> 128);
            a0 &= U128_MAX;
        }

        uint256 r = (((rM - rsub21) << 128) + _am - rsub0) >> shift;

        //  `_aM / _b` is qM from the original algorithm, inlined here to reduce stack usage
        return (q + _aM / _b, r);
    }

    /// @dev Absolute value of a 25-bit integer.
    /// @param _x the integer
    /// @return _x if _x>=0 or -_x if not
    function _abs(int256 _x) private pure returns (int256) {
        if (_x >= 0) {
            return _x;
        }
        return -_x;
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "viaIR": true,
  "evmVersion": "paris",
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {
    "contracts/Lock.sol": {
      "LockLib": "0xa8738ae018c03e69d8479aedfafbd32c4290669b"
    }
  }
}

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payable","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"uint256","name":"","type":"uint256"}],"name":"IPs","outputs":[{"internalType":"address payable","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"uint256","name":"","type":"uint256"}],"name":"OPs","outputs":[{"internalType":"address payable","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"TIME_SPAN","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"}],"name":"balance","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"}],"name":"checkRequirementsAndStart","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"uint256","name":"","type":"uint256"},{"internalType":"uint256","name":"","type":"uint256"},{"internalType":"uint256","name":"","type":"uint256"}],"name":"commitments","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"}],"name":"confirmedRewardPerOP","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"}],"name":"createMessageHash","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"address","name":"","type":"address"}],"name":"endpoints","outputs":[{"internalType":"string","name":"spdz","type":"string"},{"internalType":"string","name":"restApi","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"}],"name":"exit","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"address","name":"","type":"address"}],"name":"index","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"purpose","type":"string"},{"internalType":"string","name":"dslHash","type":"string"},{"internalType":"string","name":"dslUri","type":"string"},{"internalType":"uint256","name":"opMin","type":"uint256"},{"internalType":"uint256","name":"opMax","type":"uint256"},{"internalType":"uint256","name":"opRecruitStart","type":"uint256"},{"internalType":"uint256","name":"opRecruitEnd","type":"uint256"},{"internalType":"uint256","name":"cpMin","type":"uint256"},{"internalType":"uint256","name":"cpMax","type":"uint256"},{"internalType":"uint256","name":"cpRewardPerUnit","type":"uint256"},{"internalType":"uint256","name":"cpRecruitStart","type":"uint256"},{"internalType":"uint256","name":"cpRecruitEnd","type":"uint256"},{"internalType":"uint256","name":"ipMin","type":"uint256"},{"internalType":"uint256","name":"ipMax","type":"uint256"},{"internalType":"uint256","name":"ipRewardPerUnit","type":"uint256"},{"internalType":"uint256","name":"ipRecruitStart","type":"uint256"},{"internalType":"uint256","name":"ipRecruitEnd","type":"uint256"},{"internalType":"string","name":"spdzEndpoint","type":"string"},{"internalType":"string","name":"restApiEndpoint","type":"string"}],"name":"initializeRound","outputs":[{"internalType":"string","name":"roundId","type":"string"}],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"}],"name":"invoke","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"nextRoundId","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"address","name":"","type":"address"}],"name":"opRewardPaid","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"policy","outputs":[{"internalType":"uint256","name":"participationFee","type":"uint256"},{"internalType":"uint256","name":"resultAccessFee","type":"uint256"},{"internalType":"uint256","name":"ipRatio","type":"uint256"},{"internalType":"uint256","name":"cpRatio","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"string","name":"spdzEndpoint","type":"string"},{"internalType":"string","name":"restApiEndpoint","type":"string"}],"name":"registerCP","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"uint256","name":"i","type":"uint256"},{"internalType":"uint256","name":"j","type":"uint256"},{"internalType":"uint256","name":"x","type":"uint256"},{"internalType":"uint256","name":"y","type":"uint256"}],"name":"registerCommitment","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"uint256[]","name":"xs","type":"uint256[]"},{"internalType":"uint256[]","name":"ys","type":"uint256[]"}],"name":"registerCommitments","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"string","name":"restApiEndpoint","type":"string"}],"name":"registerIP","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"string","name":"spdzEndpoint","type":"string"},{"internalType":"string","name":"restApiEndpoint","type":"string"}],"name":"registerOP","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"uint256","name":"j","type":"uint256"},{"internalType":"uint256[]","name":"ts","type":"uint256[]"},{"internalType":"uint256[]","name":"ws","type":"uint256[]"}],"name":"registerShare","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"uint256[]","name":"ts","type":"uint256[]"},{"internalType":"uint256[]","name":"ws","type":"uint256[]"}],"name":"registerShares","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"uint256","name":"j","type":"uint256"},{"internalType":"bytes","name":"signature","type":"bytes"}],"name":"registerSignature","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"roundId","type":"string"},{"internalType":"bytes[]","name":"_signatures","type":"bytes[]"}],"name":"registerSignatures","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"}],"name":"roundConfigs","outputs":[{"internalType":"string","name":"purpose","type":"string"},{"internalType":"string","name":"dslHash","type":"string"},{"internalType":"string","name":"dslUri","type":"string"},{"internalType":"address payable","name":"pop","type":"address"},{"components":[{"internalType":"uint256","name":"minCount","type":"uint256"},{"internalType":"uint256","name":"maxCount","type":"uint256"},{"internalType":"uint256","name":"recruitStart","type":"uint256"},{"internalType":"uint256","name":"recruitEnd","type":"uint256"}],"internalType":"struct Lock.PartyRequirement","name":"opReq","type":"tuple"},{"components":[{"internalType":"uint256","name":"minCount","type":"uint256"},{"internalType":"uint256","name":"maxCount","type":"uint256"},{"internalType":"uint256","name":"recruitStart","type":"uint256"},{"internalType":"uint256","name":"recruitEnd","type":"uint256"}],"internalType":"struct Lock.PartyRequirement","name":"cpReq","type":"tuple"},{"components":[{"internalType":"uint256","name":"minCount","type":"uint256"},{"internalType":"uint256","name":"maxCount","type":"uint256"},{"internalType":"uint256","name":"recruitStart","type":"uint256"},{"internalType":"uint256","name":"recruitEnd","type":"uint256"}],"internalType":"struct Lock.PartyRequirement","name":"ipReq","type":"tuple"},{"internalType":"uint256","name":"cpRewardPerUnit","type":"uint256"},{"internalType":"uint256","name":"ipRewardPerUnit","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"uint256","name":"","type":"uint256"},{"internalType":"uint256","name":"","type":"uint256"},{"internalType":"uint256","name":"","type":"uint256"}],"name":"shares","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"},{"internalType":"uint256","name":"","type":"uint256"}],"name":"signatures","outputs":[{"internalType":"bytes","name":"","type":"bytes"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"string","name":"","type":"string"}],"name":"state","outputs":[{"internalType":"enum Lock.State","name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"timeLimit","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"withdraw","outputs":[],"stateMutability":"nonpayable","type":"function"}]

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