// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (security/ReentrancyGuard.sol)
pragma solidity ^0.8.0;
/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.
    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;
    uint256 private _status;
    constructor() {
        _status = _NOT_ENTERED;
    }
    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }
    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }
    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
}
/**
 ** Account-Abstraction (EIP-4337) singleton EntryPoint implementation.
 ** Only one instance required on each chain.
 **/
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable avoid-low-level-calls */
/* solhint-disable no-inline-assembly */
import "../interfaces/IAccount.sol";
import "../interfaces/IPaymaster.sol";
import "../interfaces/IEntryPoint.sol";
import "../utils/Exec.sol";
import "./StakeManager.sol";
import "./SenderCreator.sol";
import "./Helpers.sol";
import "./NonceManager.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
contract EntryPoint is IEntryPoint, StakeManager, NonceManager, ReentrancyGuard {
    using UserOperationLib for UserOperation;
    SenderCreator private immutable senderCreator = new SenderCreator();
    // internal value used during simulation: need to query aggregator.
    address private constant SIMULATE_FIND_AGGREGATOR = address(1);
    // marker for inner call revert on out of gas
    bytes32 private constant INNER_OUT_OF_GAS = hex'deaddead';
    uint256 private constant REVERT_REASON_MAX_LEN = 2048;
    /**
     * for simulation purposes, validateUserOp (and validatePaymasterUserOp) must return this value
     * in case of signature failure, instead of revert.
     */
    uint256 public constant SIG_VALIDATION_FAILED = 1;
    /**
     * compensate the caller's beneficiary address with the collected fees of all UserOperations.
     * @param beneficiary the address to receive the fees
     * @param amount amount to transfer.
     */
    function _compensate(address payable beneficiary, uint256 amount) internal {
        require(beneficiary != address(0), "AA90 invalid beneficiary");
        (bool success,) = beneficiary.call{value : amount}("");
        require(success, "AA91 failed send to beneficiary");
    }
    /**
     * execute a user op
     * @param opIndex index into the opInfo array
     * @param userOp the userOp to execute
     * @param opInfo the opInfo filled by validatePrepayment for this userOp.
     * @return collected the total amount this userOp paid.
     */
    function _executeUserOp(uint256 opIndex, UserOperation calldata userOp, UserOpInfo memory opInfo) private returns (uint256 collected) {
        uint256 preGas = gasleft();
        bytes memory context = getMemoryBytesFromOffset(opInfo.contextOffset);
        try this.innerHandleOp(userOp.callData, opInfo, context) returns (uint256 _actualGasCost) {
            collected = _actualGasCost;
        } catch {
            bytes32 innerRevertCode;
            assembly {
                returndatacopy(0, 0, 32)
                innerRevertCode := mload(0)
            }
            // handleOps was called with gas limit too low. abort entire bundle.
            if (innerRevertCode == INNER_OUT_OF_GAS) {
                //report paymaster, since if it is not deliberately caused by the bundler,
                // it must be a revert caused by paymaster.
                revert FailedOp(opIndex, "AA95 out of gas");
            }
            uint256 actualGas = preGas - gasleft() + opInfo.preOpGas;
            collected = _handlePostOp(opIndex, IPaymaster.PostOpMode.postOpReverted, opInfo, context, actualGas);
        }
    }
    /**
     * Execute a batch of UserOperations.
     * no signature aggregator is used.
     * if any account requires an aggregator (that is, it returned an aggregator when
     * performing simulateValidation), then handleAggregatedOps() must be used instead.
     * @param ops the operations to execute
     * @param beneficiary the address to receive the fees
     */
    function handleOps(UserOperation[] calldata ops, address payable beneficiary) public nonReentrant {
        uint256 opslen = ops.length;
        UserOpInfo[] memory opInfos = new UserOpInfo[](opslen);
    unchecked {
        for (uint256 i = 0; i < opslen; i++) {
            UserOpInfo memory opInfo = opInfos[i];
            (uint256 validationData, uint256 pmValidationData) = _validatePrepayment(i, ops[i], opInfo);
            _validateAccountAndPaymasterValidationData(i, validationData, pmValidationData, address(0));
        }
        uint256 collected = 0;
        emit BeforeExecution();
        for (uint256 i = 0; i < opslen; i++) {
            collected += _executeUserOp(i, ops[i], opInfos[i]);
        }
        _compensate(beneficiary, collected);
    } //unchecked
    }
    /**
     * Execute a batch of UserOperation with Aggregators
     * @param opsPerAggregator the operations to execute, grouped by aggregator (or address(0) for no-aggregator accounts)
     * @param beneficiary the address to receive the fees
     */
    function handleAggregatedOps(
        UserOpsPerAggregator[] calldata opsPerAggregator,
        address payable beneficiary
    ) public nonReentrant {
        uint256 opasLen = opsPerAggregator.length;
        uint256 totalOps = 0;
        for (uint256 i = 0; i < opasLen; i++) {
            UserOpsPerAggregator calldata opa = opsPerAggregator[i];
            UserOperation[] calldata ops = opa.userOps;
            IAggregator aggregator = opa.aggregator;
            //address(1) is special marker of "signature error"
            require(address(aggregator) != address(1), "AA96 invalid aggregator");
            if (address(aggregator) != address(0)) {
                // solhint-disable-next-line no-empty-blocks
                try aggregator.validateSignatures(ops, opa.signature) {}
                catch {
                    revert SignatureValidationFailed(address(aggregator));
                }
            }
            totalOps += ops.length;
        }
        UserOpInfo[] memory opInfos = new UserOpInfo[](totalOps);
        emit BeforeExecution();
        uint256 opIndex = 0;
        for (uint256 a = 0; a < opasLen; a++) {
            UserOpsPerAggregator calldata opa = opsPerAggregator[a];
            UserOperation[] calldata ops = opa.userOps;
            IAggregator aggregator = opa.aggregator;
            uint256 opslen = ops.length;
            for (uint256 i = 0; i < opslen; i++) {
                UserOpInfo memory opInfo = opInfos[opIndex];
                (uint256 validationData, uint256 paymasterValidationData) = _validatePrepayment(opIndex, ops[i], opInfo);
                _validateAccountAndPaymasterValidationData(i, validationData, paymasterValidationData, address(aggregator));
                opIndex++;
            }
        }
        uint256 collected = 0;
        opIndex = 0;
        for (uint256 a = 0; a < opasLen; a++) {
            UserOpsPerAggregator calldata opa = opsPerAggregator[a];
            emit SignatureAggregatorChanged(address(opa.aggregator));
            UserOperation[] calldata ops = opa.userOps;
            uint256 opslen = ops.length;
            for (uint256 i = 0; i < opslen; i++) {
                collected += _executeUserOp(opIndex, ops[i], opInfos[opIndex]);
                opIndex++;
            }
        }
        emit SignatureAggregatorChanged(address(0));
        _compensate(beneficiary, collected);
    }
    /// @inheritdoc IEntryPoint
    function simulateHandleOp(UserOperation calldata op, address target, bytes calldata targetCallData) external override {
        UserOpInfo memory opInfo;
        _simulationOnlyValidations(op);
        (uint256 validationData, uint256 paymasterValidationData) = _validatePrepayment(0, op, opInfo);
        ValidationData memory data = _intersectTimeRange(validationData, paymasterValidationData);
        numberMarker();
        uint256 paid = _executeUserOp(0, op, opInfo);
        numberMarker();
        bool targetSuccess;
        bytes memory targetResult;
        if (target != address(0)) {
            (targetSuccess, targetResult) = target.call(targetCallData);
        }
        revert ExecutionResult(opInfo.preOpGas, paid, data.validAfter, data.validUntil, targetSuccess, targetResult);
    }
    // A memory copy of UserOp static fields only.
    // Excluding: callData, initCode and signature. Replacing paymasterAndData with paymaster.
    struct MemoryUserOp {
        address sender;
        uint256 nonce;
        uint256 callGasLimit;
        uint256 verificationGasLimit;
        uint256 preVerificationGas;
        address paymaster;
        uint256 maxFeePerGas;
        uint256 maxPriorityFeePerGas;
    }
    struct UserOpInfo {
        MemoryUserOp mUserOp;
        bytes32 userOpHash;
        uint256 prefund;
        uint256 contextOffset;
        uint256 preOpGas;
    }
    /**
     * inner function to handle a UserOperation.
     * Must be declared "external" to open a call context, but it can only be called by handleOps.
     */
    function innerHandleOp(bytes memory callData, UserOpInfo memory opInfo, bytes calldata context) external returns (uint256 actualGasCost) {
        uint256 preGas = gasleft();
        require(msg.sender == address(this), "AA92 internal call only");
        MemoryUserOp memory mUserOp = opInfo.mUserOp;
        uint callGasLimit = mUserOp.callGasLimit;
    unchecked {
        // handleOps was called with gas limit too low. abort entire bundle.
        if (gasleft() < callGasLimit + mUserOp.verificationGasLimit + 5000) {
            assembly {
                mstore(0, INNER_OUT_OF_GAS)
                revert(0, 32)
            }
        }
    }
        IPaymaster.PostOpMode mode = IPaymaster.PostOpMode.opSucceeded;
        if (callData.length > 0) {
            bool success = Exec.call(mUserOp.sender, 0, callData, callGasLimit);
            if (!success) {
                bytes memory result = Exec.getReturnData(REVERT_REASON_MAX_LEN);
                if (result.length > 0) {
                    emit UserOperationRevertReason(opInfo.userOpHash, mUserOp.sender, mUserOp.nonce, result);
                }
                mode = IPaymaster.PostOpMode.opReverted;
            }
        }
    unchecked {
        uint256 actualGas = preGas - gasleft() + opInfo.preOpGas;
        //note: opIndex is ignored (relevant only if mode==postOpReverted, which is only possible outside of innerHandleOp)
        return _handlePostOp(0, mode, opInfo, context, actualGas);
    }
    }
    /**
     * generate a request Id - unique identifier for this request.
     * the request ID is a hash over the content of the userOp (except the signature), the entrypoint and the chainid.
     */
    function getUserOpHash(UserOperation calldata userOp) public view returns (bytes32) {
        return keccak256(abi.encode(userOp.hash(), address(this), block.chainid));
    }
    /**
     * copy general fields from userOp into the memory opInfo structure.
     */
    function _copyUserOpToMemory(UserOperation calldata userOp, MemoryUserOp memory mUserOp) internal pure {
        mUserOp.sender = userOp.sender;
        mUserOp.nonce = userOp.nonce;
        mUserOp.callGasLimit = userOp.callGasLimit;
        mUserOp.verificationGasLimit = userOp.verificationGasLimit;
        mUserOp.preVerificationGas = userOp.preVerificationGas;
        mUserOp.maxFeePerGas = userOp.maxFeePerGas;
        mUserOp.maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        bytes calldata paymasterAndData = userOp.paymasterAndData;
        if (paymasterAndData.length > 0) {
            require(paymasterAndData.length >= 20, "AA93 invalid paymasterAndData");
            mUserOp.paymaster = address(bytes20(paymasterAndData[: 20]));
        } else {
            mUserOp.paymaster = address(0);
        }
    }
    /**
     * Simulate a call to account.validateUserOp and paymaster.validatePaymasterUserOp.
     * @dev this method always revert. Successful result is ValidationResult error. other errors are failures.
     * @dev The node must also verify it doesn't use banned opcodes, and that it doesn't reference storage outside the account's data.
     * @param userOp the user operation to validate.
     */
    function simulateValidation(UserOperation calldata userOp) external {
        UserOpInfo memory outOpInfo;
        _simulationOnlyValidations(userOp);
        (uint256 validationData, uint256 paymasterValidationData) = _validatePrepayment(0, userOp, outOpInfo);
        StakeInfo memory paymasterInfo = _getStakeInfo(outOpInfo.mUserOp.paymaster);
        StakeInfo memory senderInfo = _getStakeInfo(outOpInfo.mUserOp.sender);
        StakeInfo memory factoryInfo;
        {
            bytes calldata initCode = userOp.initCode;
            address factory = initCode.length >= 20 ? address(bytes20(initCode[0 : 20])) : address(0);
            factoryInfo = _getStakeInfo(factory);
        }
        ValidationData memory data = _intersectTimeRange(validationData, paymasterValidationData);
        address aggregator = data.aggregator;
        bool sigFailed = aggregator == address(1);
        ReturnInfo memory returnInfo = ReturnInfo(outOpInfo.preOpGas, outOpInfo.prefund,
            sigFailed, data.validAfter, data.validUntil, getMemoryBytesFromOffset(outOpInfo.contextOffset));
        if (aggregator != address(0) && aggregator != address(1)) {
            AggregatorStakeInfo memory aggregatorInfo = AggregatorStakeInfo(aggregator, _getStakeInfo(aggregator));
            revert ValidationResultWithAggregation(returnInfo, senderInfo, factoryInfo, paymasterInfo, aggregatorInfo);
        }
        revert ValidationResult(returnInfo, senderInfo, factoryInfo, paymasterInfo);
    }
    function _getRequiredPrefund(MemoryUserOp memory mUserOp) internal pure returns (uint256 requiredPrefund) {
    unchecked {
        //when using a Paymaster, the verificationGasLimit is used also to as a limit for the postOp call.
        // our security model might call postOp eventually twice
        uint256 mul = mUserOp.paymaster != address(0) ? 3 : 1;
        uint256 requiredGas = mUserOp.callGasLimit + mUserOp.verificationGasLimit * mul + mUserOp.preVerificationGas;
        requiredPrefund = requiredGas * mUserOp.maxFeePerGas;
    }
    }
    // create the sender's contract if needed.
    function _createSenderIfNeeded(uint256 opIndex, UserOpInfo memory opInfo, bytes calldata initCode) internal {
        if (initCode.length != 0) {
            address sender = opInfo.mUserOp.sender;
            if (sender.code.length != 0) revert FailedOp(opIndex, "AA10 sender already constructed");
            address sender1 = senderCreator.createSender{gas : opInfo.mUserOp.verificationGasLimit}(initCode);
            if (sender1 == address(0)) revert FailedOp(opIndex, "AA13 initCode failed or OOG");
            if (sender1 != sender) revert FailedOp(opIndex, "AA14 initCode must return sender");
            if (sender1.code.length == 0) revert FailedOp(opIndex, "AA15 initCode must create sender");
            address factory = address(bytes20(initCode[0 : 20]));
            emit AccountDeployed(opInfo.userOpHash, sender, factory, opInfo.mUserOp.paymaster);
        }
    }
    /**
     * Get counterfactual sender address.
     *  Calculate the sender contract address that will be generated by the initCode and salt in the UserOperation.
     * this method always revert, and returns the address in SenderAddressResult error
     * @param initCode the constructor code to be passed into the UserOperation.
     */
    function getSenderAddress(bytes calldata initCode) public {
        address sender = senderCreator.createSender(initCode);
        revert SenderAddressResult(sender);
    }
    function _simulationOnlyValidations(UserOperation calldata userOp) internal view {
        // solhint-disable-next-line no-empty-blocks
        try this._validateSenderAndPaymaster(userOp.initCode, userOp.sender, userOp.paymasterAndData) {}
        catch Error(string memory revertReason) {
            if (bytes(revertReason).length != 0) {
                revert FailedOp(0, revertReason);
            }
        }
    }
    /**
    * Called only during simulation.
    * This function always reverts to prevent warm/cold storage differentiation in simulation vs execution.
    */
    function _validateSenderAndPaymaster(bytes calldata initCode, address sender, bytes calldata paymasterAndData) external view {
        if (initCode.length == 0 && sender.code.length == 0) {
            // it would revert anyway. but give a meaningful message
            revert("AA20 account not deployed");
        }
        if (paymasterAndData.length >= 20) {
            address paymaster = address(bytes20(paymasterAndData[0 : 20]));
            if (paymaster.code.length == 0) {
                // it would revert anyway. but give a meaningful message
                revert("AA30 paymaster not deployed");
            }
        }
        // always revert
        revert("");
    }
    /**
     * call account.validateUserOp.
     * revert (with FailedOp) in case validateUserOp reverts, or account didn't send required prefund.
     * decrement account's deposit if needed
     */
    function _validateAccountPrepayment(uint256 opIndex, UserOperation calldata op, UserOpInfo memory opInfo, uint256 requiredPrefund)
    internal returns (uint256 gasUsedByValidateAccountPrepayment, uint256 validationData) {
    unchecked {
        uint256 preGas = gasleft();
        MemoryUserOp memory mUserOp = opInfo.mUserOp;
        address sender = mUserOp.sender;
        _createSenderIfNeeded(opIndex, opInfo, op.initCode);
        address paymaster = mUserOp.paymaster;
        numberMarker();
        uint256 missingAccountFunds = 0;
        if (paymaster == address(0)) {
            uint256 bal = balanceOf(sender);
            missingAccountFunds = bal > requiredPrefund ? 0 : requiredPrefund - bal;
        }
        try IAccount(sender).validateUserOp{gas : mUserOp.verificationGasLimit}(op, opInfo.userOpHash, missingAccountFunds)
        returns (uint256 _validationData) {
            validationData = _validationData;
        } catch Error(string memory revertReason) {
            revert FailedOp(opIndex, string.concat("AA23 reverted: ", revertReason));
        } catch {
            revert FailedOp(opIndex, "AA23 reverted (or OOG)");
        }
        if (paymaster == address(0)) {
            DepositInfo storage senderInfo = deposits[sender];
            uint256 deposit = senderInfo.deposit;
            if (requiredPrefund > deposit) {
                revert FailedOp(opIndex, "AA21 didn't pay prefund");
            }
            senderInfo.deposit = uint112(deposit - requiredPrefund);
        }
        gasUsedByValidateAccountPrepayment = preGas - gasleft();
    }
    }
    /**
     * In case the request has a paymaster:
     * Validate paymaster has enough deposit.
     * Call paymaster.validatePaymasterUserOp.
     * Revert with proper FailedOp in case paymaster reverts.
     * Decrement paymaster's deposit
     */
    function _validatePaymasterPrepayment(uint256 opIndex, UserOperation calldata op, UserOpInfo memory opInfo, uint256 requiredPreFund, uint256 gasUsedByValidateAccountPrepayment)
    internal returns (bytes memory context, uint256 validationData) {
    unchecked {
        MemoryUserOp memory mUserOp = opInfo.mUserOp;
        uint256 verificationGasLimit = mUserOp.verificationGasLimit;
        require(verificationGasLimit > gasUsedByValidateAccountPrepayment, "AA41 too little verificationGas");
        uint256 gas = verificationGasLimit - gasUsedByValidateAccountPrepayment;
        address paymaster = mUserOp.paymaster;
        DepositInfo storage paymasterInfo = deposits[paymaster];
        uint256 deposit = paymasterInfo.deposit;
        if (deposit < requiredPreFund) {
            revert FailedOp(opIndex, "AA31 paymaster deposit too low");
        }
        paymasterInfo.deposit = uint112(deposit - requiredPreFund);
        try IPaymaster(paymaster).validatePaymasterUserOp{gas : gas}(op, opInfo.userOpHash, requiredPreFund) returns (bytes memory _context, uint256 _validationData){
            context = _context;
            validationData = _validationData;
        } catch Error(string memory revertReason) {
            revert FailedOp(opIndex, string.concat("AA33 reverted: ", revertReason));
        } catch {
            revert FailedOp(opIndex, "AA33 reverted (or OOG)");
        }
    }
    }
    /**
     * revert if either account validationData or paymaster validationData is expired
     */
    function _validateAccountAndPaymasterValidationData(uint256 opIndex, uint256 validationData, uint256 paymasterValidationData, address expectedAggregator) internal view {
        (address aggregator, bool outOfTimeRange) = _getValidationData(validationData);
        if (expectedAggregator != aggregator) {
            revert FailedOp(opIndex, "AA24 signature error");
        }
        if (outOfTimeRange) {
            revert FailedOp(opIndex, "AA22 expired or not due");
        }
        //pmAggregator is not a real signature aggregator: we don't have logic to handle it as address.
        // non-zero address means that the paymaster fails due to some signature check (which is ok only during estimation)
        address pmAggregator;
        (pmAggregator, outOfTimeRange) = _getValidationData(paymasterValidationData);
        if (pmAggregator != address(0)) {
            revert FailedOp(opIndex, "AA34 signature error");
        }
        if (outOfTimeRange) {
            revert FailedOp(opIndex, "AA32 paymaster expired or not due");
        }
    }
    function _getValidationData(uint256 validationData) internal view returns (address aggregator, bool outOfTimeRange) {
        if (validationData == 0) {
            return (address(0), false);
        }
        ValidationData memory data = _parseValidationData(validationData);
        // solhint-disable-next-line not-rely-on-time
        outOfTimeRange = block.timestamp > data.validUntil || block.timestamp < data.validAfter;
        aggregator = data.aggregator;
    }
    /**
     * validate account and paymaster (if defined).
     * also make sure total validation doesn't exceed verificationGasLimit
     * this method is called off-chain (simulateValidation()) and on-chain (from handleOps)
     * @param opIndex the index of this userOp into the "opInfos" array
     * @param userOp the userOp to validate
     */
    function _validatePrepayment(uint256 opIndex, UserOperation calldata userOp, UserOpInfo memory outOpInfo)
    private returns (uint256 validationData, uint256 paymasterValidationData) {
        uint256 preGas = gasleft();
        MemoryUserOp memory mUserOp = outOpInfo.mUserOp;
        _copyUserOpToMemory(userOp, mUserOp);
        outOpInfo.userOpHash = getUserOpHash(userOp);
        // validate all numeric values in userOp are well below 128 bit, so they can safely be added
        // and multiplied without causing overflow
        uint256 maxGasValues = mUserOp.preVerificationGas | mUserOp.verificationGasLimit | mUserOp.callGasLimit |
        userOp.maxFeePerGas | userOp.maxPriorityFeePerGas;
        require(maxGasValues <= type(uint120).max, "AA94 gas values overflow");
        uint256 gasUsedByValidateAccountPrepayment;
        (uint256 requiredPreFund) = _getRequiredPrefund(mUserOp);
        (gasUsedByValidateAccountPrepayment, validationData) = _validateAccountPrepayment(opIndex, userOp, outOpInfo, requiredPreFund);
        if (!_validateAndUpdateNonce(mUserOp.sender, mUserOp.nonce)) {
            revert FailedOp(opIndex, "AA25 invalid account nonce");
        }
        //a "marker" where account opcode validation is done and paymaster opcode validation is about to start
        // (used only by off-chain simulateValidation)
        numberMarker();
        bytes memory context;
        if (mUserOp.paymaster != address(0)) {
            (context, paymasterValidationData) = _validatePaymasterPrepayment(opIndex, userOp, outOpInfo, requiredPreFund, gasUsedByValidateAccountPrepayment);
        }
    unchecked {
        uint256 gasUsed = preGas - gasleft();
        if (userOp.verificationGasLimit < gasUsed) {
            revert FailedOp(opIndex, "AA40 over verificationGasLimit");
        }
        outOpInfo.prefund = requiredPreFund;
        outOpInfo.contextOffset = getOffsetOfMemoryBytes(context);
        outOpInfo.preOpGas = preGas - gasleft() + userOp.preVerificationGas;
    }
    }
    /**
     * process post-operation.
     * called just after the callData is executed.
     * if a paymaster is defined and its validation returned a non-empty context, its postOp is called.
     * the excess amount is refunded to the account (or paymaster - if it was used in the request)
     * @param opIndex index in the batch
     * @param mode - whether is called from innerHandleOp, or outside (postOpReverted)
     * @param opInfo userOp fields and info collected during validation
     * @param context the context returned in validatePaymasterUserOp
     * @param actualGas the gas used so far by this user operation
     */
    function _handlePostOp(uint256 opIndex, IPaymaster.PostOpMode mode, UserOpInfo memory opInfo, bytes memory context, uint256 actualGas) private returns (uint256 actualGasCost) {
        uint256 preGas = gasleft();
    unchecked {
        address refundAddress;
        MemoryUserOp memory mUserOp = opInfo.mUserOp;
        uint256 gasPrice = getUserOpGasPrice(mUserOp);
        address paymaster = mUserOp.paymaster;
        if (paymaster == address(0)) {
            refundAddress = mUserOp.sender;
        } else {
            refundAddress = paymaster;
            if (context.length > 0) {
                actualGasCost = actualGas * gasPrice;
                if (mode != IPaymaster.PostOpMode.postOpReverted) {
                    IPaymaster(paymaster).postOp{gas : mUserOp.verificationGasLimit}(mode, context, actualGasCost);
                } else {
                    // solhint-disable-next-line no-empty-blocks
                    try IPaymaster(paymaster).postOp{gas : mUserOp.verificationGasLimit}(mode, context, actualGasCost) {}
                    catch Error(string memory reason) {
                        revert FailedOp(opIndex, string.concat("AA50 postOp reverted: ", reason));
                    }
                    catch {
                        revert FailedOp(opIndex, "AA50 postOp revert");
                    }
                }
            }
        }
        actualGas += preGas - gasleft();
        actualGasCost = actualGas * gasPrice;
        if (opInfo.prefund < actualGasCost) {
            revert FailedOp(opIndex, "AA51 prefund below actualGasCost");
        }
        uint256 refund = opInfo.prefund - actualGasCost;
        _incrementDeposit(refundAddress, refund);
        bool success = mode == IPaymaster.PostOpMode.opSucceeded;
        emit UserOperationEvent(opInfo.userOpHash, mUserOp.sender, mUserOp.paymaster, mUserOp.nonce, success, actualGasCost, actualGas);
    } // unchecked
    }
    /**
     * the gas price this UserOp agrees to pay.
     * relayer/block builder might submit the TX with higher priorityFee, but the user should not
     */
    function getUserOpGasPrice(MemoryUserOp memory mUserOp) internal view returns (uint256) {
    unchecked {
        uint256 maxFeePerGas = mUserOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = mUserOp.maxPriorityFeePerGas;
        if (maxFeePerGas == maxPriorityFeePerGas) {
            //legacy mode (for networks that don't support basefee opcode)
            return maxFeePerGas;
        }
        return min(maxFeePerGas, maxPriorityFeePerGas + block.basefee);
    }
    }
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    function getOffsetOfMemoryBytes(bytes memory data) internal pure returns (uint256 offset) {
        assembly {offset := data}
    }
    function getMemoryBytesFromOffset(uint256 offset) internal pure returns (bytes memory data) {
        assembly {data := offset}
    }
    //place the NUMBER opcode in the code.
    // this is used as a marker during simulation, as this OP is completely banned from the simulated code of the
    // account and paymaster.
    function numberMarker() internal view {
        assembly {mstore(0, number())}
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
/**
 * returned data from validateUserOp.
 * validateUserOp returns a uint256, with is created by `_packedValidationData` and parsed by `_parseValidationData`
 * @param aggregator - address(0) - the account validated the signature by itself.
 *              address(1) - the account failed to validate the signature.
 *              otherwise - this is an address of a signature aggregator that must be used to validate the signature.
 * @param validAfter - this UserOp is valid only after this timestamp.
 * @param validaUntil - this UserOp is valid only up to this timestamp.
 */
    struct ValidationData {
        address aggregator;
        uint48 validAfter;
        uint48 validUntil;
    }
//extract sigFailed, validAfter, validUntil.
// also convert zero validUntil to type(uint48).max
    function _parseValidationData(uint validationData) pure returns (ValidationData memory data) {
        address aggregator = address(uint160(validationData));
        uint48 validUntil = uint48(validationData >> 160);
        if (validUntil == 0) {
            validUntil = type(uint48).max;
        }
        uint48 validAfter = uint48(validationData >> (48 + 160));
        return ValidationData(aggregator, validAfter, validUntil);
    }
// intersect account and paymaster ranges.
    function _intersectTimeRange(uint256 validationData, uint256 paymasterValidationData) pure returns (ValidationData memory) {
        ValidationData memory accountValidationData = _parseValidationData(validationData);
        ValidationData memory pmValidationData = _parseValidationData(paymasterValidationData);
        address aggregator = accountValidationData.aggregator;
        if (aggregator == address(0)) {
            aggregator = pmValidationData.aggregator;
        }
        uint48 validAfter = accountValidationData.validAfter;
        uint48 validUntil = accountValidationData.validUntil;
        uint48 pmValidAfter = pmValidationData.validAfter;
        uint48 pmValidUntil = pmValidationData.validUntil;
        if (validAfter < pmValidAfter) validAfter = pmValidAfter;
        if (validUntil > pmValidUntil) validUntil = pmValidUntil;
        return ValidationData(aggregator, validAfter, validUntil);
    }
/**
 * helper to pack the return value for validateUserOp
 * @param data - the ValidationData to pack
 */
    function _packValidationData(ValidationData memory data) pure returns (uint256) {
        return uint160(data.aggregator) | (uint256(data.validUntil) << 160) | (uint256(data.validAfter) << (160 + 48));
    }
/**
 * helper to pack the return value for validateUserOp, when not using an aggregator
 * @param sigFailed - true for signature failure, false for success
 * @param validUntil last timestamp this UserOperation is valid (or zero for infinite)
 * @param validAfter first timestamp this UserOperation is valid
 */
    function _packValidationData(bool sigFailed, uint48 validUntil, uint48 validAfter) pure returns (uint256) {
        return (sigFailed ? 1 : 0) | (uint256(validUntil) << 160) | (uint256(validAfter) << (160 + 48));
    }
/**
 * keccak function over calldata.
 * @dev copy calldata into memory, do keccak and drop allocated memory. Strangely, this is more efficient than letting solidity do it.
 */
    function calldataKeccak(bytes calldata data) pure returns (bytes32 ret) {
        assembly {
            let mem := mload(0x40)
            let len := data.length
            calldatacopy(mem, data.offset, len)
            ret := keccak256(mem, len)
        }
    }
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "../interfaces/IEntryPoint.sol";
/**
 * nonce management functionality
 */
contract NonceManager is INonceManager {
    /**
     * The next valid sequence number for a given nonce key.
     */
    mapping(address => mapping(uint192 => uint256)) public nonceSequenceNumber;
    function getNonce(address sender, uint192 key)
    public view override returns (uint256 nonce) {
        return nonceSequenceNumber[sender][key] | (uint256(key) << 64);
    }
    // allow an account to manually increment its own nonce.
    // (mainly so that during construction nonce can be made non-zero,
    // to "absorb" the gas cost of first nonce increment to 1st transaction (construction),
    // not to 2nd transaction)
    function incrementNonce(uint192 key) public override {
        nonceSequenceNumber[msg.sender][key]++;
    }
    /**
     * validate nonce uniqueness for this account.
     * called just after validateUserOp()
     */
    function _validateAndUpdateNonce(address sender, uint256 nonce) internal returns (bool) {
        uint192 key = uint192(nonce >> 64);
        uint64 seq = uint64(nonce);
        return nonceSequenceNumber[sender][key]++ == seq;
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/**
 * helper contract for EntryPoint, to call userOp.initCode from a "neutral" address,
 * which is explicitly not the entryPoint itself.
 */
contract SenderCreator {
    /**
     * call the "initCode" factory to create and return the sender account address
     * @param initCode the initCode value from a UserOp. contains 20 bytes of factory address, followed by calldata
     * @return sender the returned address of the created account, or zero address on failure.
     */
    function createSender(bytes calldata initCode) external returns (address sender) {
        address factory = address(bytes20(initCode[0 : 20]));
        bytes memory initCallData = initCode[20 :];
        bool success;
        /* solhint-disable no-inline-assembly */
        assembly {
            success := call(gas(), factory, 0, add(initCallData, 0x20), mload(initCallData), 0, 32)
            sender := mload(0)
        }
        if (!success) {
            sender = address(0);
        }
    }
}
// SPDX-License-Identifier: GPL-3.0-only
pragma solidity ^0.8.12;
import "../interfaces/IStakeManager.sol";
/* solhint-disable avoid-low-level-calls */
/* solhint-disable not-rely-on-time */
/**
 * manage deposits and stakes.
 * deposit is just a balance used to pay for UserOperations (either by a paymaster or an account)
 * stake is value locked for at least "unstakeDelay" by a paymaster.
 */
abstract contract StakeManager is IStakeManager {
    /// maps paymaster to their deposits and stakes
    mapping(address => DepositInfo) public deposits;
    /// @inheritdoc IStakeManager
    function getDepositInfo(address account) public view returns (DepositInfo memory info) {
        return deposits[account];
    }
    // internal method to return just the stake info
    function _getStakeInfo(address addr) internal view returns (StakeInfo memory info) {
        DepositInfo storage depositInfo = deposits[addr];
        info.stake = depositInfo.stake;
        info.unstakeDelaySec = depositInfo.unstakeDelaySec;
    }
    /// return the deposit (for gas payment) of the account
    function balanceOf(address account) public view returns (uint256) {
        return deposits[account].deposit;
    }
    receive() external payable {
        depositTo(msg.sender);
    }
    function _incrementDeposit(address account, uint256 amount) internal {
        DepositInfo storage info = deposits[account];
        uint256 newAmount = info.deposit + amount;
        require(newAmount <= type(uint112).max, "deposit overflow");
        info.deposit = uint112(newAmount);
    }
    /**
     * add to the deposit of the given account
     */
    function depositTo(address account) public payable {
        _incrementDeposit(account, msg.value);
        DepositInfo storage info = deposits[account];
        emit Deposited(account, info.deposit);
    }
    /**
     * add to the account's stake - amount and delay
     * any pending unstake is first cancelled.
     * @param unstakeDelaySec the new lock duration before the deposit can be withdrawn.
     */
    function addStake(uint32 unstakeDelaySec) public payable {
        DepositInfo storage info = deposits[msg.sender];
        require(unstakeDelaySec > 0, "must specify unstake delay");
        require(unstakeDelaySec >= info.unstakeDelaySec, "cannot decrease unstake time");
        uint256 stake = info.stake + msg.value;
        require(stake > 0, "no stake specified");
        require(stake <= type(uint112).max, "stake overflow");
        deposits[msg.sender] = DepositInfo(
            info.deposit,
            true,
            uint112(stake),
            unstakeDelaySec,
            0
        );
        emit StakeLocked(msg.sender, stake, unstakeDelaySec);
    }
    /**
     * attempt to unlock the stake.
     * the value can be withdrawn (using withdrawStake) after the unstake delay.
     */
    function unlockStake() external {
        DepositInfo storage info = deposits[msg.sender];
        require(info.unstakeDelaySec != 0, "not staked");
        require(info.staked, "already unstaking");
        uint48 withdrawTime = uint48(block.timestamp) + info.unstakeDelaySec;
        info.withdrawTime = withdrawTime;
        info.staked = false;
        emit StakeUnlocked(msg.sender, withdrawTime);
    }
    /**
     * withdraw from the (unlocked) stake.
     * must first call unlockStake and wait for the unstakeDelay to pass
     * @param withdrawAddress the address to send withdrawn value.
     */
    function withdrawStake(address payable withdrawAddress) external {
        DepositInfo storage info = deposits[msg.sender];
        uint256 stake = info.stake;
        require(stake > 0, "No stake to withdraw");
        require(info.withdrawTime > 0, "must call unlockStake() first");
        require(info.withdrawTime <= block.timestamp, "Stake withdrawal is not due");
        info.unstakeDelaySec = 0;
        info.withdrawTime = 0;
        info.stake = 0;
        emit StakeWithdrawn(msg.sender, withdrawAddress, stake);
        (bool success,) = withdrawAddress.call{value : stake}("");
        require(success, "failed to withdraw stake");
    }
    /**
     * withdraw from the deposit.
     * @param withdrawAddress the address to send withdrawn value.
     * @param withdrawAmount the amount to withdraw.
     */
    function withdrawTo(address payable withdrawAddress, uint256 withdrawAmount) external {
        DepositInfo storage info = deposits[msg.sender];
        require(withdrawAmount <= info.deposit, "Withdraw amount too large");
        info.deposit = uint112(info.deposit - withdrawAmount);
        emit Withdrawn(msg.sender, withdrawAddress, withdrawAmount);
        (bool success,) = withdrawAddress.call{value : withdrawAmount}("");
        require(success, "failed to withdraw");
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
interface IAccount {
    /**
     * Validate user's signature and nonce
     * the entryPoint will make the call to the recipient only if this validation call returns successfully.
     * signature failure should be reported by returning SIG_VALIDATION_FAILED (1).
     * This allows making a "simulation call" without a valid signature
     * Other failures (e.g. nonce mismatch, or invalid signature format) should still revert to signal failure.
     *
     * @dev Must validate caller is the entryPoint.
     *      Must validate the signature and nonce
     * @param userOp the operation that is about to be executed.
     * @param userOpHash hash of the user's request data. can be used as the basis for signature.
     * @param missingAccountFunds missing funds on the account's deposit in the entrypoint.
     *      This is the minimum amount to transfer to the sender(entryPoint) to be able to make the call.
     *      The excess is left as a deposit in the entrypoint, for future calls.
     *      can be withdrawn anytime using "entryPoint.withdrawTo()"
     *      In case there is a paymaster in the request (or the current deposit is high enough), this value will be zero.
     * @return validationData packaged ValidationData structure. use `_packValidationData` and `_unpackValidationData` to encode and decode
     *      <20-byte> sigAuthorizer - 0 for valid signature, 1 to mark signature failure,
     *         otherwise, an address of an "authorizer" contract.
     *      <6-byte> validUntil - last timestamp this operation is valid. 0 for "indefinite"
     *      <6-byte> validAfter - first timestamp this operation is valid
     *      If an account doesn't use time-range, it is enough to return SIG_VALIDATION_FAILED value (1) for signature failure.
     *      Note that the validation code cannot use block.timestamp (or block.number) directly.
     */
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
    external returns (uint256 validationData);
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
/**
 * Aggregated Signatures validator.
 */
interface IAggregator {
    /**
     * validate aggregated signature.
     * revert if the aggregated signature does not match the given list of operations.
     */
    function validateSignatures(UserOperation[] calldata userOps, bytes calldata signature) external view;
    /**
     * validate signature of a single userOp
     * This method is should be called by bundler after EntryPoint.simulateValidation() returns (reverts) with ValidationResultWithAggregation
     * First it validates the signature over the userOp. Then it returns data to be used when creating the handleOps.
     * @param userOp the userOperation received from the user.
     * @return sigForUserOp the value to put into the signature field of the userOp when calling handleOps.
     *    (usually empty, unless account and aggregator support some kind of "multisig"
     */
    function validateUserOpSignature(UserOperation calldata userOp)
    external view returns (bytes memory sigForUserOp);
    /**
     * aggregate multiple signatures into a single value.
     * This method is called off-chain to calculate the signature to pass with handleOps()
     * bundler MAY use optimized custom code perform this aggregation
     * @param userOps array of UserOperations to collect the signatures from.
     * @return aggregatedSignature the aggregated signature
     */
    function aggregateSignatures(UserOperation[] calldata userOps) external view returns (bytes memory aggregatedSignature);
}
/**
 ** Account-Abstraction (EIP-4337) singleton EntryPoint implementation.
 ** Only one instance required on each chain.
 **/
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable avoid-low-level-calls */
/* solhint-disable no-inline-assembly */
/* solhint-disable reason-string */
import "./UserOperation.sol";
import "./IStakeManager.sol";
import "./IAggregator.sol";
import "./INonceManager.sol";
interface IEntryPoint is IStakeManager, INonceManager {
    /***
     * An event emitted after each successful request
     * @param userOpHash - unique identifier for the request (hash its entire content, except signature).
     * @param sender - the account that generates this request.
     * @param paymaster - if non-null, the paymaster that pays for this request.
     * @param nonce - the nonce value from the request.
     * @param success - true if the sender transaction succeeded, false if reverted.
     * @param actualGasCost - actual amount paid (by account or paymaster) for this UserOperation.
     * @param actualGasUsed - total gas used by this UserOperation (including preVerification, creation, validation and execution).
     */
    event UserOperationEvent(bytes32 indexed userOpHash, address indexed sender, address indexed paymaster, uint256 nonce, bool success, uint256 actualGasCost, uint256 actualGasUsed);
    /**
     * account "sender" was deployed.
     * @param userOpHash the userOp that deployed this account. UserOperationEvent will follow.
     * @param sender the account that is deployed
     * @param factory the factory used to deploy this account (in the initCode)
     * @param paymaster the paymaster used by this UserOp
     */
    event AccountDeployed(bytes32 indexed userOpHash, address indexed sender, address factory, address paymaster);
    /**
     * An event emitted if the UserOperation "callData" reverted with non-zero length
     * @param userOpHash the request unique identifier.
     * @param sender the sender of this request
     * @param nonce the nonce used in the request
     * @param revertReason - the return bytes from the (reverted) call to "callData".
     */
    event UserOperationRevertReason(bytes32 indexed userOpHash, address indexed sender, uint256 nonce, bytes revertReason);
    /**
     * an event emitted by handleOps(), before starting the execution loop.
     * any event emitted before this event, is part of the validation.
     */
    event BeforeExecution();
    /**
     * signature aggregator used by the following UserOperationEvents within this bundle.
     */
    event SignatureAggregatorChanged(address indexed aggregator);
    /**
     * a custom revert error of handleOps, to identify the offending op.
     *  NOTE: if simulateValidation passes successfully, there should be no reason for handleOps to fail on it.
     *  @param opIndex - index into the array of ops to the failed one (in simulateValidation, this is always zero)
     *  @param reason - revert reason
     *      The string starts with a unique code "AAmn", where "m" is "1" for factory, "2" for account and "3" for paymaster issues,
     *      so a failure can be attributed to the correct entity.
     *   Should be caught in off-chain handleOps simulation and not happen on-chain.
     *   Useful for mitigating DoS attempts against batchers or for troubleshooting of factory/account/paymaster reverts.
     */
    error FailedOp(uint256 opIndex, string reason);
    /**
     * error case when a signature aggregator fails to verify the aggregated signature it had created.
     */
    error SignatureValidationFailed(address aggregator);
    /**
     * Successful result from simulateValidation.
     * @param returnInfo gas and time-range returned values
     * @param senderInfo stake information about the sender
     * @param factoryInfo stake information about the factory (if any)
     * @param paymasterInfo stake information about the paymaster (if any)
     */
    error ValidationResult(ReturnInfo returnInfo,
        StakeInfo senderInfo, StakeInfo factoryInfo, StakeInfo paymasterInfo);
    /**
     * Successful result from simulateValidation, if the account returns a signature aggregator
     * @param returnInfo gas and time-range returned values
     * @param senderInfo stake information about the sender
     * @param factoryInfo stake information about the factory (if any)
     * @param paymasterInfo stake information about the paymaster (if any)
     * @param aggregatorInfo signature aggregation info (if the account requires signature aggregator)
     *      bundler MUST use it to verify the signature, or reject the UserOperation
     */
    error ValidationResultWithAggregation(ReturnInfo returnInfo,
        StakeInfo senderInfo, StakeInfo factoryInfo, StakeInfo paymasterInfo,
        AggregatorStakeInfo aggregatorInfo);
    /**
     * return value of getSenderAddress
     */
    error SenderAddressResult(address sender);
    /**
     * return value of simulateHandleOp
     */
    error ExecutionResult(uint256 preOpGas, uint256 paid, uint48 validAfter, uint48 validUntil, bool targetSuccess, bytes targetResult);
    //UserOps handled, per aggregator
    struct UserOpsPerAggregator {
        UserOperation[] userOps;
        // aggregator address
        IAggregator aggregator;
        // aggregated signature
        bytes signature;
    }
    /**
     * Execute a batch of UserOperation.
     * no signature aggregator is used.
     * if any account requires an aggregator (that is, it returned an aggregator when
     * performing simulateValidation), then handleAggregatedOps() must be used instead.
     * @param ops the operations to execute
     * @param beneficiary the address to receive the fees
     */
    function handleOps(UserOperation[] calldata ops, address payable beneficiary) external;
    /**
     * Execute a batch of UserOperation with Aggregators
     * @param opsPerAggregator the operations to execute, grouped by aggregator (or address(0) for no-aggregator accounts)
     * @param beneficiary the address to receive the fees
     */
    function handleAggregatedOps(
        UserOpsPerAggregator[] calldata opsPerAggregator,
        address payable beneficiary
    ) external;
    /**
     * generate a request Id - unique identifier for this request.
     * the request ID is a hash over the content of the userOp (except the signature), the entrypoint and the chainid.
     */
    function getUserOpHash(UserOperation calldata userOp) external view returns (bytes32);
    /**
     * Simulate a call to account.validateUserOp and paymaster.validatePaymasterUserOp.
     * @dev this method always revert. Successful result is ValidationResult error. other errors are failures.
     * @dev The node must also verify it doesn't use banned opcodes, and that it doesn't reference storage outside the account's data.
     * @param userOp the user operation to validate.
     */
    function simulateValidation(UserOperation calldata userOp) external;
    /**
     * gas and return values during simulation
     * @param preOpGas the gas used for validation (including preValidationGas)
     * @param prefund the required prefund for this operation
     * @param sigFailed validateUserOp's (or paymaster's) signature check failed
     * @param validAfter - first timestamp this UserOp is valid (merging account and paymaster time-range)
     * @param validUntil - last timestamp this UserOp is valid (merging account and paymaster time-range)
     * @param paymasterContext returned by validatePaymasterUserOp (to be passed into postOp)
     */
    struct ReturnInfo {
        uint256 preOpGas;
        uint256 prefund;
        bool sigFailed;
        uint48 validAfter;
        uint48 validUntil;
        bytes paymasterContext;
    }
    /**
     * returned aggregated signature info.
     * the aggregator returned by the account, and its current stake.
     */
    struct AggregatorStakeInfo {
        address aggregator;
        StakeInfo stakeInfo;
    }
    /**
     * Get counterfactual sender address.
     *  Calculate the sender contract address that will be generated by the initCode and salt in the UserOperation.
     * this method always revert, and returns the address in SenderAddressResult error
     * @param initCode the constructor code to be passed into the UserOperation.
     */
    function getSenderAddress(bytes memory initCode) external;
    /**
     * simulate full execution of a UserOperation (including both validation and target execution)
     * this method will always revert with "ExecutionResult".
     * it performs full validation of the UserOperation, but ignores signature error.
     * an optional target address is called after the userop succeeds, and its value is returned
     * (before the entire call is reverted)
     * Note that in order to collect the the success/failure of the target call, it must be executed
     * with trace enabled to track the emitted events.
     * @param op the UserOperation to simulate
     * @param target if nonzero, a target address to call after userop simulation. If called, the targetSuccess and targetResult
     *        are set to the return from that call.
     * @param targetCallData callData to pass to target address
     */
    function simulateHandleOp(UserOperation calldata op, address target, bytes calldata targetCallData) external;
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
interface INonceManager {
    /**
     * Return the next nonce for this sender.
     * Within a given key, the nonce values are sequenced (starting with zero, and incremented by one on each userop)
     * But UserOp with different keys can come with arbitrary order.
     *
     * @param sender the account address
     * @param key the high 192 bit of the nonce
     * @return nonce a full nonce to pass for next UserOp with this sender.
     */
    function getNonce(address sender, uint192 key)
    external view returns (uint256 nonce);
    /**
     * Manually increment the nonce of the sender.
     * This method is exposed just for completeness..
     * Account does NOT need to call it, neither during validation, nor elsewhere,
     * as the EntryPoint will update the nonce regardless.
     * Possible use-case is call it with various keys to "initialize" their nonces to one, so that future
     * UserOperations will not pay extra for the first transaction with a given key.
     */
    function incrementNonce(uint192 key) external;
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
/**
 * the interface exposed by a paymaster contract, who agrees to pay the gas for user's operations.
 * a paymaster must hold a stake to cover the required entrypoint stake and also the gas for the transaction.
 */
interface IPaymaster {
    enum PostOpMode {
        opSucceeded, // user op succeeded
        opReverted, // user op reverted. still has to pay for gas.
        postOpReverted //user op succeeded, but caused postOp to revert. Now it's a 2nd call, after user's op was deliberately reverted.
    }
    /**
     * payment validation: check if paymaster agrees to pay.
     * Must verify sender is the entryPoint.
     * Revert to reject this request.
     * Note that bundlers will reject this method if it changes the state, unless the paymaster is trusted (whitelisted)
     * The paymaster pre-pays using its deposit, and receive back a refund after the postOp method returns.
     * @param userOp the user operation
     * @param userOpHash hash of the user's request data.
     * @param maxCost the maximum cost of this transaction (based on maximum gas and gas price from userOp)
     * @return context value to send to a postOp
     *      zero length to signify postOp is not required.
     * @return validationData signature and time-range of this operation, encoded the same as the return value of validateUserOperation
     *      <20-byte> sigAuthorizer - 0 for valid signature, 1 to mark signature failure,
     *         otherwise, an address of an "authorizer" contract.
     *      <6-byte> validUntil - last timestamp this operation is valid. 0 for "indefinite"
     *      <6-byte> validAfter - first timestamp this operation is valid
     *      Note that the validation code cannot use block.timestamp (or block.number) directly.
     */
    function validatePaymasterUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 maxCost)
    external returns (bytes memory context, uint256 validationData);
    /**
     * post-operation handler.
     * Must verify sender is the entryPoint
     * @param mode enum with the following options:
     *      opSucceeded - user operation succeeded.
     *      opReverted  - user op reverted. still has to pay for gas.
     *      postOpReverted - user op succeeded, but caused postOp (in mode=opSucceeded) to revert.
     *                       Now this is the 2nd call, after user's op was deliberately reverted.
     * @param context - the context value returned by validatePaymasterUserOp
     * @param actualGasCost - actual gas used so far (without this postOp call).
     */
    function postOp(PostOpMode mode, bytes calldata context, uint256 actualGasCost) external;
}
// SPDX-License-Identifier: GPL-3.0-only
pragma solidity ^0.8.12;
/**
 * manage deposits and stakes.
 * deposit is just a balance used to pay for UserOperations (either by a paymaster or an account)
 * stake is value locked for at least "unstakeDelay" by the staked entity.
 */
interface IStakeManager {
    event Deposited(
        address indexed account,
        uint256 totalDeposit
    );
    event Withdrawn(
        address indexed account,
        address withdrawAddress,
        uint256 amount
    );
    /// Emitted when stake or unstake delay are modified
    event StakeLocked(
        address indexed account,
        uint256 totalStaked,
        uint256 unstakeDelaySec
    );
    /// Emitted once a stake is scheduled for withdrawal
    event StakeUnlocked(
        address indexed account,
        uint256 withdrawTime
    );
    event StakeWithdrawn(
        address indexed account,
        address withdrawAddress,
        uint256 amount
    );
    /**
     * @param deposit the entity's deposit
     * @param staked true if this entity is staked.
     * @param stake actual amount of ether staked for this entity.
     * @param unstakeDelaySec minimum delay to withdraw the stake.
     * @param withdrawTime - first block timestamp where 'withdrawStake' will be callable, or zero if already locked
     * @dev sizes were chosen so that (deposit,staked, stake) fit into one cell (used during handleOps)
     *    and the rest fit into a 2nd cell.
     *    112 bit allows for 10^15 eth
     *    48 bit for full timestamp
     *    32 bit allows 150 years for unstake delay
     */
    struct DepositInfo {
        uint112 deposit;
        bool staked;
        uint112 stake;
        uint32 unstakeDelaySec;
        uint48 withdrawTime;
    }
    //API struct used by getStakeInfo and simulateValidation
    struct StakeInfo {
        uint256 stake;
        uint256 unstakeDelaySec;
    }
    /// @return info - full deposit information of given account
    function getDepositInfo(address account) external view returns (DepositInfo memory info);
    /// @return the deposit (for gas payment) of the account
    function balanceOf(address account) external view returns (uint256);
    /**
     * add to the deposit of the given account
     */
    function depositTo(address account) external payable;
    /**
     * add to the account's stake - amount and delay
     * any pending unstake is first cancelled.
     * @param _unstakeDelaySec the new lock duration before the deposit can be withdrawn.
     */
    function addStake(uint32 _unstakeDelaySec) external payable;
    /**
     * attempt to unlock the stake.
     * the value can be withdrawn (using withdrawStake) after the unstake delay.
     */
    function unlockStake() external;
    /**
     * withdraw from the (unlocked) stake.
     * must first call unlockStake and wait for the unstakeDelay to pass
     * @param withdrawAddress the address to send withdrawn value.
     */
    function withdrawStake(address payable withdrawAddress) external;
    /**
     * withdraw from the deposit.
     * @param withdrawAddress the address to send withdrawn value.
     * @param withdrawAmount the amount to withdraw.
     */
    function withdrawTo(address payable withdrawAddress, uint256 withdrawAmount) external;
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
import {calldataKeccak} from "../core/Helpers.sol";
/**
 * User Operation struct
 * @param sender the sender account of this request.
     * @param nonce unique value the sender uses to verify it is not a replay.
     * @param initCode if set, the account contract will be created by this constructor/
     * @param callData the method call to execute on this account.
     * @param callGasLimit the gas limit passed to the callData method call.
     * @param verificationGasLimit gas used for validateUserOp and validatePaymasterUserOp.
     * @param preVerificationGas gas not calculated by the handleOps method, but added to the gas paid. Covers batch overhead.
     * @param maxFeePerGas same as EIP-1559 gas parameter.
     * @param maxPriorityFeePerGas same as EIP-1559 gas parameter.
     * @param paymasterAndData if set, this field holds the paymaster address and paymaster-specific data. the paymaster will pay for the transaction instead of the sender.
     * @param signature sender-verified signature over the entire request, the EntryPoint address and the chain ID.
     */
    struct UserOperation {
        address sender;
        uint256 nonce;
        bytes initCode;
        bytes callData;
        uint256 callGasLimit;
        uint256 verificationGasLimit;
        uint256 preVerificationGas;
        uint256 maxFeePerGas;
        uint256 maxPriorityFeePerGas;
        bytes paymasterAndData;
        bytes signature;
    }
/**
 * Utility functions helpful when working with UserOperation structs.
 */
library UserOperationLib {
    function getSender(UserOperation calldata userOp) internal pure returns (address) {
        address data;
        //read sender from userOp, which is first userOp member (saves 800 gas...)
        assembly {data := calldataload(userOp)}
        return address(uint160(data));
    }
    //relayer/block builder might submit the TX with higher priorityFee, but the user should not
    // pay above what he signed for.
    function gasPrice(UserOperation calldata userOp) internal view returns (uint256) {
    unchecked {
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        if (maxFeePerGas == maxPriorityFeePerGas) {
            //legacy mode (for networks that don't support basefee opcode)
            return maxFeePerGas;
        }
        return min(maxFeePerGas, maxPriorityFeePerGas + block.basefee);
    }
    }
    function pack(UserOperation calldata userOp) internal pure returns (bytes memory ret) {
        address sender = getSender(userOp);
        uint256 nonce = userOp.nonce;
        bytes32 hashInitCode = calldataKeccak(userOp.initCode);
        bytes32 hashCallData = calldataKeccak(userOp.callData);
        uint256 callGasLimit = userOp.callGasLimit;
        uint256 verificationGasLimit = userOp.verificationGasLimit;
        uint256 preVerificationGas = userOp.preVerificationGas;
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        bytes32 hashPaymasterAndData = calldataKeccak(userOp.paymasterAndData);
        return abi.encode(
            sender, nonce,
            hashInitCode, hashCallData,
            callGasLimit, verificationGasLimit, preVerificationGas,
            maxFeePerGas, maxPriorityFeePerGas,
            hashPaymasterAndData
        );
    }
    function hash(UserOperation calldata userOp) internal pure returns (bytes32) {
        return keccak256(pack(userOp));
    }
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
}
// SPDX-License-Identifier: LGPL-3.0-only
pragma solidity >=0.7.5 <0.9.0;
// solhint-disable no-inline-assembly
/**
 * Utility functions helpful when making different kinds of contract calls in Solidity.
 */
library Exec {
    function call(
        address to,
        uint256 value,
        bytes memory data,
        uint256 txGas
    ) internal returns (bool success) {
        assembly {
            success := call(txGas, to, value, add(data, 0x20), mload(data), 0, 0)
        }
    }
    function staticcall(
        address to,
        bytes memory data,
        uint256 txGas
    ) internal view returns (bool success) {
        assembly {
            success := staticcall(txGas, to, add(data, 0x20), mload(data), 0, 0)
        }
    }
    function delegateCall(
        address to,
        bytes memory data,
        uint256 txGas
    ) internal returns (bool success) {
        assembly {
            success := delegatecall(txGas, to, add(data, 0x20), mload(data), 0, 0)
        }
    }
    // get returned data from last call or calldelegate
    function getReturnData(uint256 maxLen) internal pure returns (bytes memory returnData) {
        assembly {
            let len := returndatasize()
            if gt(len, maxLen) {
                len := maxLen
            }
            let ptr := mload(0x40)
            mstore(0x40, add(ptr, add(len, 0x20)))
            mstore(ptr, len)
            returndatacopy(add(ptr, 0x20), 0, len)
            returnData := ptr
        }
    }
    // revert with explicit byte array (probably reverted info from call)
    function revertWithData(bytes memory returnData) internal pure {
        assembly {
            revert(add(returnData, 32), mload(returnData))
        }
    }
    function callAndRevert(address to, bytes memory data, uint256 maxLen) internal {
        bool success = call(to,0,data,gasleft());
        if (!success) {
            revertWithData(getReturnData(maxLen));
        }
    }
}

// Copyright (C) 2015, 2016, 2017 Dapphub

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.4.18;

contract WETH9 {
    string public name     = "Wrapped Ether";
    string public symbol   = "WETH";
    uint8  public decimals = 18;

    event  Approval(address indexed src, address indexed guy, uint wad);
    event  Transfer(address indexed src, address indexed dst, uint wad);
    event  Deposit(address indexed dst, uint wad);
    event  Withdrawal(address indexed src, uint wad);

    mapping (address => uint)                       public  balanceOf;
    mapping (address => mapping (address => uint))  public  allowance;

    function() public payable {
        deposit();
    }
    function deposit() public payable {
        balanceOf[msg.sender] += msg.value;
        Deposit(msg.sender, msg.value);
    }
    function withdraw(uint wad) public {
        require(balanceOf[msg.sender] >= wad);
        balanceOf[msg.sender] -= wad;
        msg.sender.transfer(wad);
        Withdrawal(msg.sender, wad);
    }

    function totalSupply() public view returns (uint) {
        return this.balance;
    }

    function approve(address guy, uint wad) public returns (bool) {
        allowance[msg.sender][guy] = wad;
        Approval(msg.sender, guy, wad);
        return true;
    }

    function transfer(address dst, uint wad) public returns (bool) {
        return transferFrom(msg.sender, dst, wad);
    }

    function transferFrom(address src, address dst, uint wad)
        public
        returns (bool)
    {
        require(balanceOf[src] >= wad);

        if (src != msg.sender && allowance[src][msg.sender] != uint(-1)) {
            require(allowance[src][msg.sender] >= wad);
            allowance[src][msg.sender] -= wad;
        }

        balanceOf[src] -= wad;
        balanceOf[dst] += wad;

        Transfer(src, dst, wad);

        return true;
    }
}


/*
                    GNU GENERAL PUBLIC LICENSE
                       Version 3, 29 June 2007

 Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.

                            Preamble

  The GNU General Public License is a free, copyleft license for
software and other kinds of works.

  The licenses for most software and other practical works are designed
to take away your freedom to share and change the works.  By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users.  We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors.  You can apply it to
your programs, too.

  When we speak of free software, we are referring to freedom, not
price.  Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.

  To protect your rights, we need to prevent others from denying you
these rights or asking you to surrender the rights.  Therefore, you have
certain responsibilities if you distribute copies of the software, or if
you modify it: responsibilities to respect the freedom of others.

  For example, if you distribute copies of such a program, whether
gratis or for a fee, you must pass on to the recipients the same
freedoms that you received.  You must make sure that they, too, receive
or can get the source code.  And you must show them these terms so they
know their rights.

  Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
giving you legal permission to copy, distribute and/or modify it.

  For the developers' and authors' protection, the GPL clearly explains
that there is no warranty for this free software.  For both users' and
authors' sake, the GPL requires that modified versions be marked as
changed, so that their problems will not be attributed erroneously to
authors of previous versions.

  Some devices are designed to deny users access to install or run
modified versions of the software inside them, although the manufacturer
can do so.  This is fundamentally incompatible with the aim of
protecting users' freedom to change the software.  The systematic
pattern of such abuse occurs in the area of products for individuals to
use, which is precisely where it is most unacceptable.  Therefore, we
have designed this version of the GPL to prohibit the practice for those
products.  If such problems arise substantially in other domains, we
stand ready to extend this provision to those domains in future versions
of the GPL, as needed to protect the freedom of users.

  Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
software on general-purpose computers, but in those that do, we wish to
avoid the special danger that patents applied to a free program could
make it effectively proprietary.  To prevent this, the GPL assures that
patents cannot be used to render the program non-free.

  The precise terms and conditions for copying, distribution and
modification follow.

                       TERMS AND CONDITIONS

  0. Definitions.

  "This License" refers to version 3 of the GNU General Public License.

  "Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.

  "The Program" refers to any copyrightable work licensed under this
License.  Each licensee is addressed as "you".  "Licensees" and
"recipients" may be individuals or organizations.

  To "modify" a work means to copy from or adapt all or part of the work
in a fashion requiring copyright permission, other than the making of an
exact copy.  The resulting work is called a "modified version" of the
earlier work or a work "based on" the earlier work.

  A "covered work" means either the unmodified Program or a work based
on the Program.

  To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
computer or modifying a private copy.  Propagation includes copying,
distribution (with or without modification), making available to the
public, and in some countries other activities as well.

  To "convey" a work means any kind of propagation that enables other
parties to make or receive copies.  Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.

  An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License.  If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.

  1. Source Code.

  The "source code" for a work means the preferred form of the work
for making modifications to it.  "Object code" means any non-source
form of a work.

  A "Standard Interface" means an interface that either is an official
standard defined by a recognized standards body, or, in the case of
interfaces specified for a particular programming language, one that
is widely used among developers working in that language.

  The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
packaging a Major Component, but which is not part of that Major
Component, and (b) serves only to enable use of the work with that
Major Component, or to implement a Standard Interface for which an
implementation is available to the public in source code form.  A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
(if any) on which the executable work runs, or a compiler used to
produce the work, or an object code interpreter used to run it.

  The "Corresponding Source" for a work in object code form means all
the source code needed to generate, install, and (for an executable
work) run the object code and to modify the work, including scripts to
control those activities.  However, it does not include the work's
System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work.  For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,
such as by intimate data communication or control flow between those
subprograms and other parts of the work.

  The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.

  The Corresponding Source for a work in source code form is that
same work.

  2. Basic Permissions.

  All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met.  This License explicitly affirms your unlimited
permission to run the unmodified Program.  The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work.  This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.

  You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force.  You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright.  Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.

  Conveying under any other circumstances is permitted solely under
the conditions stated below.  Sublicensing is not allowed; section 10
makes it unnecessary.

  3. Protecting Users' Legal Rights From Anti-Circumvention Law.

  No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.

  When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.

  4. Conveying Verbatim Copies.

  You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.

  You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.

  5. Conveying Modified Source Versions.

  You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:

    a) The work must carry prominent notices stating that you modified
    it, and giving a relevant date.

    b) The work must carry prominent notices stating that it is
    released under this License and any conditions added under section
    7.  This requirement modifies the requirement in section 4 to
    "keep intact all notices".

    c) You must license the entire work, as a whole, under this
    License to anyone who comes into possession of a copy.  This
    License will therefore apply, along with any applicable section 7
    additional terms, to the whole of the work, and all its parts,
    regardless of how they are packaged.  This License gives no
    permission to license the work in any other way, but it does not
    invalidate such permission if you have separately received it.

    d) If the work has interactive user interfaces, each must display
    Appropriate Legal Notices; however, if the Program has interactive
    interfaces that do not display Appropriate Legal Notices, your
    work need not make them do so.

  A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit.  Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.

  6. Conveying Non-Source Forms.

  You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:

    a) Convey the object code in, or embodied in, a physical product
    (including a physical distribution medium), accompanied by the
    Corresponding Source fixed on a durable physical medium
    customarily used for software interchange.

    b) Convey the object code in, or embodied in, a physical product
    (including a physical distribution medium), accompanied by a
    written offer, valid for at least three years and valid for as
    long as you offer spare parts or customer support for that product
    model, to give anyone who possesses the object code either (1) a
    copy of the Corresponding Source for all the software in the
    product that is covered by this License, on a durable physical
    medium customarily used for software interchange, for a price no
    more than your reasonable cost of physically performing this
    conveying of source, or (2) access to copy the
    Corresponding Source from a network server at no charge.

    c) Convey individual copies of the object code with a copy of the
    written offer to provide the Corresponding Source.  This
    alternative is allowed only occasionally and noncommercially, and
    only if you received the object code with such an offer, in accord
    with subsection 6b.

    d) Convey the object code by offering access from a designated
    place (gratis or for a charge), and offer equivalent access to the
    Corresponding Source in the same way through the same place at no
    further charge.  You need not require recipients to copy the
    Corresponding Source along with the object code.  If the place to
    copy the object code is a network server, the Corresponding Source
    may be on a different server (operated by you or a third party)
    that supports equivalent copying facilities, provided you maintain
    clear directions next to the object code saying where to find the
    Corresponding Source.  Regardless of what server hosts the
    Corresponding Source, you remain obligated to ensure that it is
    available for as long as needed to satisfy these requirements.

    e) Convey the object code using peer-to-peer transmission, provided
    you inform other peers where the object code and Corresponding
    Source of the work are being offered to the general public at no
    charge under subsection 6d.

  A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.

  A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling.  In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage.  For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product.  A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

  "Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source.  The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.

  If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information.  But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).

  The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed.  Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.

  Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.

  7. Additional Terms.

  "Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law.  If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.

  When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it.  (Additional permissions may be written to require their own
removal in certain cases when you modify the work.)  You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.

  Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:

    a) Disclaiming warranty or limiting liability differently from the
    terms of sections 15 and 16 of this License; or

    b) Requiring preservation of specified reasonable legal notices or
    author attributions in that material or in the Appropriate Legal
    Notices displayed by works containing it; or

    c) Prohibiting misrepresentation of the origin of that material, or
    requiring that modified versions of such material be marked in
    reasonable ways as different from the original version; or

    d) Limiting the use for publicity purposes of names of licensors or
    authors of the material; or

    e) Declining to grant rights under trademark law for use of some
    trade names, trademarks, or service marks; or

    f) Requiring indemnification of licensors and authors of that
    material by anyone who conveys the material (or modified versions of
    it) with contractual assumptions of liability to the recipient, for
    any liability that these contractual assumptions directly impose on
    those licensors and authors.

  All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10.  If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term.  If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.

  If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.

  Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.

  8. Termination.

  You may not propagate or modify a covered work except as expressly
provided under this License.  Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).

  However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.

  Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.

  Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License.  If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.

  9. Acceptance Not Required for Having Copies.

  You are not required to accept this License in order to receive or
run a copy of the Program.  Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance.  However,
nothing other than this License grants you permission to propagate or
modify any covered work.  These actions infringe copyright if you do
not accept this License.  Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.

  10. Automatic Licensing of Downstream Recipients.

  Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License.  You are not responsible
for enforcing compliance by third parties with this License.

  An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations.  If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.

  You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License.  For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.

  11. Patents.

  A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based.  The
work thus licensed is called the contributor's "contributor version".

  A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version.  For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.

  Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.

  In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement).  To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.

  If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients.  "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.

  If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.

  A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License.  You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.

  Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.

  12. No Surrender of Others' Freedom.

  If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License.  If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all.  For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.

  13. Use with the GNU Affero General Public License.

  Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
combined work, and to convey the resulting work.  The terms of this
License will continue to apply to the part which is the covered work,
but the special requirements of the GNU Affero General Public License,
section 13, concerning interaction through a network will apply to the
combination as such.

  14. Revised Versions of this License.

  The Free Software Foundation may publish revised and/or new versions of
the GNU General Public License from time to time.  Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.

  Each version is given a distinguishing version number.  If the
Program specifies that a certain numbered version of the GNU General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation.  If the Program does not specify a version number of the
GNU General Public License, you may choose any version ever published
by the Free Software Foundation.

  If the Program specifies that a proxy can decide which future
versions of the GNU General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.

  Later license versions may give you additional or different
permissions.  However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.

  15. Disclaimer of Warranty.

  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

  16. Limitation of Liability.

  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.

  17. Interpretation of Sections 15 and 16.

  If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.

                     END OF TERMS AND CONDITIONS

            How to Apply These Terms to Your New Programs

  If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.

  To do so, attach the following notices to the program.  It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.

    <one line to give the program's name and a brief idea of what it does.>
    Copyright (C) <year>  <name of author>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail.

  If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:

    <program>  Copyright (C) <year>  <name of author>
    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License.  Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".

  You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.

  The GNU General Public License does not permit incorporating your program
into proprietary programs.  If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library.  If this is what you want to do, use the GNU Lesser General
Public License instead of this License.  But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

*/

// SPDX-License-Identifier: MIT
pragma solidity 0.8.23;
import {IAccount} from "account-abstraction/interfaces/IAccount.sol";
import {UserOperation, UserOperationLib} from "account-abstraction/interfaces/UserOperation.sol";
import {Receiver} from "solady/accounts/Receiver.sol";
import {SignatureCheckerLib} from "solady/utils/SignatureCheckerLib.sol";
import {UUPSUpgradeable} from "solady/utils/UUPSUpgradeable.sol";
import {WebAuthn} from "webauthn-sol/WebAuthn.sol";
import {ERC1271} from "./ERC1271.sol";
import {MultiOwnable} from "./MultiOwnable.sol";
/// @title Coinbase Smart Wallet
///
/// @notice ERC-4337-compatible smart account, based on Solady's ERC4337 account implementation
///         with inspiration from Alchemy's LightAccount and Daimo's DaimoAccount. Verified by z0r0z.eth from (⌘) NANI.eth
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC4337.sol)
contract CoinbaseSmartWallet is ERC1271, IAccount, MultiOwnable, UUPSUpgradeable, Receiver {
    /// @notice A wrapper struct used for signature validation so that callers
    ///         can identify the owner that signed.
    struct SignatureWrapper {
        /// @dev The index of the owner that signed, see `MultiOwnable.ownerAtIndex`
        uint256 ownerIndex;
        /// @dev If `MultiOwnable.ownerAtIndex` is an Ethereum address, this should be `abi.encodePacked(r, s, v)`
        ///      If `MultiOwnable.ownerAtIndex` is a public key, this should be `abi.encode(WebAuthnAuth)`.
        bytes signatureData;
    }
    /// @notice Represents a call to make.
    struct Call {
        /// @dev The address to call.
        address target;
        /// @dev The value to send when making the call.
        uint256 value;
        /// @dev The data of the call.
        bytes data;
    }
    /// @notice Reserved nonce key (upper 192 bits of `UserOperation.nonce`) for cross-chain replayable
    ///         transactions.
    ///
    /// @dev MUST BE the `UserOperation.nonce` key when `UserOperation.calldata` is calling
    ///      `executeWithoutChainIdValidation`and MUST NOT BE `UserOperation.nonce` key when `UserOperation.calldata` is
    ///      NOT calling `executeWithoutChainIdValidation`.
    ///
    /// @dev Helps enforce sequential sequencing of replayable transactions.
    uint256 public constant REPLAYABLE_NONCE_KEY = 8453;
    /// @notice Thrown when `initialize` is called but the account already has had at least one owner.
    error Initialized();
    /// @notice Thrown when a call is passed to `executeWithoutChainIdValidation` that is not allowed by
    ///         `canSkipChainIdValidation`
    ///
    /// @param selector The selector of the call.
    error SelectorNotAllowed(bytes4 selector);
    /// @notice Thrown in validateUserOp if the key of `UserOperation.nonce` does not match the calldata.
    ///
    /// @dev Calls to `this.executeWithoutChainIdValidation` MUST use `REPLAYABLE_NONCE_KEY` and
    ///      calls NOT to `this.executeWithoutChainIdValidation` MUST NOT use `REPLAYABLE_NONCE_KEY`.
    ///
    /// @param key The invalid `UserOperation.nonce` key.
    error InvalidNonceKey(uint256 key);
    /// @notice Reverts if the caller is not the EntryPoint.
    modifier onlyEntryPoint() virtual {
        if (msg.sender != entryPoint()) {
            revert Unauthorized();
        }
        _;
    }
    /// @notice Reverts if the caller is neither the EntryPoint, the owner, nor the account itself.
    modifier onlyEntryPointOrOwner() virtual {
        if (msg.sender != entryPoint()) {
            _checkOwner();
        }
        _;
    }
    /// @notice Sends to the EntryPoint (i.e. `msg.sender`) the missing funds for this transaction.
    ///
    /// @dev Subclass MAY override this modifier for better funds management (e.g. send to the
    ///      EntryPoint more than the minimum required, so that in future transactions it will not
    ///      be required to send again).
    ///
    /// @param missingAccountFunds The minimum value this modifier should send the EntryPoint which
    ///                            MAY be zero, in case there is enough deposit, or the userOp has a
    ///                            paymaster.
    modifier payPrefund(uint256 missingAccountFunds) virtual {
        _;
        assembly ("memory-safe") {
            if missingAccountFunds {
                // Ignore failure (it's EntryPoint's job to verify, not the account's).
                pop(call(gas(), caller(), missingAccountFunds, codesize(), 0x00, codesize(), 0x00))
            }
        }
    }
    constructor() {
        // Implementation should not be initializable (does not affect proxies which use their own storage).
        bytes[] memory owners = new bytes[](1);
        owners[0] = abi.encode(address(0));
        _initializeOwners(owners);
    }
    /// @notice Initializes the account with the `owners`.
    ///
    /// @dev Reverts if the account has had at least one owner, i.e. has been initialized.
    ///
    /// @param owners Array of initial owners for this account. Each item should be
    ///               an ABI encoded Ethereum address, i.e. 32 bytes with 12 leading 0 bytes,
    ///               or a 64 byte public key.
    function initialize(bytes[] calldata owners) external payable virtual {
        if (nextOwnerIndex() != 0) {
            revert Initialized();
        }
        _initializeOwners(owners);
    }
    /// @inheritdoc IAccount
    ///
    /// @notice ERC-4337 `validateUserOp` method. The EntryPoint will
    ///         call `UserOperation.sender.call(UserOperation.callData)` only if this validation call returns
    ///         successfully.
    ///
    /// @dev Signature failure should be reported by returning 1 (see: `this._isValidSignature`). This
    ///      allows making a "simulation call" without a valid signature. Other failures (e.g. invalid signature format)
    ///      should still revert to signal failure.
    /// @dev Reverts if the `UserOperation.nonce` key is invalid for `UserOperation.calldata`.
    /// @dev Reverts if the signature format is incorrect or invalid for owner type.
    ///
    /// @param userOp              The `UserOperation` to validate.
    /// @param userOpHash          The `UserOperation` hash, as computed by `EntryPoint.getUserOpHash(UserOperation)`.
    /// @param missingAccountFunds The missing account funds that must be deposited on the Entrypoint.
    ///
    /// @return validationData The encoded `ValidationData` structure:
    ///                        `(uint256(validAfter) << (160 + 48)) | (uint256(validUntil) << 160) | (success ? 0 : 1)`
    ///                        where `validUntil` is 0 (indefinite) and `validAfter` is 0.
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
        external
        virtual
        onlyEntryPoint
        payPrefund(missingAccountFunds)
        returns (uint256 validationData)
    {
        uint256 key = userOp.nonce >> 64;
        if (bytes4(userOp.callData) == this.executeWithoutChainIdValidation.selector) {
            userOpHash = getUserOpHashWithoutChainId(userOp);
            if (key != REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        } else {
            if (key == REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        }
        // Return 0 if the recovered address matches the owner.
        if (_isValidSignature(userOpHash, userOp.signature)) {
            return 0;
        }
        // Else return 1
        return 1;
    }
    /// @notice Executes `calls` on this account (i.e. self call).
    ///
    /// @dev Can only be called by the Entrypoint.
    /// @dev Reverts if the given call is not authorized to skip the chain ID validtion.
    /// @dev `validateUserOp()` will recompute the `userOpHash` without the chain ID before validating
    ///      it if the `UserOperation.calldata` is calling this function. This allows certain UserOperations
    ///      to be replayed for all accounts sharing the same address across chains. E.g. This may be
    ///      useful for syncing owner changes.
    ///
    /// @param calls An array of calldata to use for separate self calls.
    function executeWithoutChainIdValidation(bytes[] calldata calls) external payable virtual onlyEntryPoint {
        for (uint256 i; i < calls.length; i++) {
            bytes calldata call = calls[i];
            bytes4 selector = bytes4(call);
            if (!canSkipChainIdValidation(selector)) {
                revert SelectorNotAllowed(selector);
            }
            _call(address(this), 0, call);
        }
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param target The address to call.
    /// @param value  The value to send with the call.
    /// @param data   The data of the call.
    function execute(address target, uint256 value, bytes calldata data)
        external
        payable
        virtual
        onlyEntryPointOrOwner
    {
        _call(target, value, data);
    }
    /// @notice Executes batch of `Call`s.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param calls The list of `Call`s to execute.
    function executeBatch(Call[] calldata calls) external payable virtual onlyEntryPointOrOwner {
        for (uint256 i; i < calls.length; i++) {
            _call(calls[i].target, calls[i].value, calls[i].data);
        }
    }
    /// @notice Returns the address of the EntryPoint v0.6.
    ///
    /// @return The address of the EntryPoint v0.6
    function entryPoint() public view virtual returns (address) {
        return 0x5FF137D4b0FDCD49DcA30c7CF57E578a026d2789;
    }
    /// @notice Computes the hash of the `UserOperation` in the same way as EntryPoint v0.6, but
    ///         leaves out the chain ID.
    ///
    /// @dev This allows accounts to sign a hash that can be used on many chains.
    ///
    /// @param userOp The `UserOperation` to compute the hash for.
    ///
    /// @return The `UserOperation` hash, which does not depend on chain ID.
    function getUserOpHashWithoutChainId(UserOperation calldata userOp) public view virtual returns (bytes32) {
        return keccak256(abi.encode(UserOperationLib.hash(userOp), entryPoint()));
    }
    /// @notice Returns the implementation of the ERC1967 proxy.
    ///
    /// @return $ The address of implementation contract.
    function implementation() public view returns (address $) {
        assembly {
            $ := sload(_ERC1967_IMPLEMENTATION_SLOT)
        }
    }
    /// @notice Returns whether `functionSelector` can be called in `executeWithoutChainIdValidation`.
    ///
    /// @param functionSelector The function selector to check.
    ////
    /// @return `true` is the function selector is allowed to skip the chain ID validation, else `false`.
    function canSkipChainIdValidation(bytes4 functionSelector) public pure returns (bool) {
        if (
            functionSelector == MultiOwnable.addOwnerPublicKey.selector
                || functionSelector == MultiOwnable.addOwnerAddress.selector
                || functionSelector == MultiOwnable.removeOwnerAtIndex.selector
                || functionSelector == MultiOwnable.removeLastOwner.selector
                || functionSelector == UUPSUpgradeable.upgradeToAndCall.selector
        ) {
            return true;
        }
        return false;
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Reverts if the call reverted.
    /// @dev Implementation taken from
    /// https://github.com/alchemyplatform/light-account/blob/43f625afdda544d5e5af9c370c9f4be0943e4e90/src/common/BaseLightAccount.sol#L125
    ///
    /// @param target The target call address.
    /// @param value  The call value to user.
    /// @param data   The raw call data.
    function _call(address target, uint256 value, bytes memory data) internal {
        (bool success, bytes memory result) = target.call{value: value}(data);
        if (!success) {
            assembly ("memory-safe") {
                revert(add(result, 32), mload(result))
            }
        }
    }
    /// @inheritdoc ERC1271
    ///
    /// @dev Used by both `ERC1271.isValidSignature` AND `IAccount.validateUserOp` signature validation.
    /// @dev Reverts if owner at `ownerIndex` is not compatible with `signature` format.
    ///
    /// @param signature ABI encoded `SignatureWrapper`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual override returns (bool) {
        SignatureWrapper memory sigWrapper = abi.decode(signature, (SignatureWrapper));
        bytes memory ownerBytes = ownerAtIndex(sigWrapper.ownerIndex);
        if (ownerBytes.length == 32) {
            if (uint256(bytes32(ownerBytes)) > type(uint160).max) {
                // technically should be impossible given owners can only be added with
                // addOwnerAddress and addOwnerPublicKey, but we leave incase of future changes.
                revert InvalidEthereumAddressOwner(ownerBytes);
            }
            address owner;
            assembly ("memory-safe") {
                owner := mload(add(ownerBytes, 32))
            }
            return SignatureCheckerLib.isValidSignatureNow(owner, hash, sigWrapper.signatureData);
        }
        if (ownerBytes.length == 64) {
            (uint256 x, uint256 y) = abi.decode(ownerBytes, (uint256, uint256));
            WebAuthn.WebAuthnAuth memory auth = abi.decode(sigWrapper.signatureData, (WebAuthn.WebAuthnAuth));
            return WebAuthn.verify({challenge: abi.encode(hash), requireUV: false, webAuthnAuth: auth, x: x, y: y});
        }
        revert InvalidOwnerBytesLength(ownerBytes);
    }
    /// @inheritdoc UUPSUpgradeable
    ///
    /// @dev Authorization logic is only based on the `msg.sender` being an owner of this account,
    ///      or `address(this)`.
    function _authorizeUpgrade(address) internal view virtual override(UUPSUpgradeable) onlyOwner {}
    /// @inheritdoc ERC1271
    function _domainNameAndVersion() internal pure override(ERC1271) returns (string memory, string memory) {
        return ("Coinbase Smart Wallet", "1");
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
interface IAccount {
    /**
     * Validate user's signature and nonce
     * the entryPoint will make the call to the recipient only if this validation call returns successfully.
     * signature failure should be reported by returning SIG_VALIDATION_FAILED (1).
     * This allows making a "simulation call" without a valid signature
     * Other failures (e.g. nonce mismatch, or invalid signature format) should still revert to signal failure.
     *
     * @dev Must validate caller is the entryPoint.
     *      Must validate the signature and nonce
     * @param userOp the operation that is about to be executed.
     * @param userOpHash hash of the user's request data. can be used as the basis for signature.
     * @param missingAccountFunds missing funds on the account's deposit in the entrypoint.
     *      This is the minimum amount to transfer to the sender(entryPoint) to be able to make the call.
     *      The excess is left as a deposit in the entrypoint, for future calls.
     *      can be withdrawn anytime using "entryPoint.withdrawTo()"
     *      In case there is a paymaster in the request (or the current deposit is high enough), this value will be zero.
     * @return validationData packaged ValidationData structure. use `_packValidationData` and `_unpackValidationData` to encode and decode
     *      <20-byte> sigAuthorizer - 0 for valid signature, 1 to mark signature failure,
     *         otherwise, an address of an "authorizer" contract.
     *      <6-byte> validUntil - last timestamp this operation is valid. 0 for "indefinite"
     *      <6-byte> validAfter - first timestamp this operation is valid
     *      If an account doesn't use time-range, it is enough to return SIG_VALIDATION_FAILED value (1) for signature failure.
     *      Note that the validation code cannot use block.timestamp (or block.number) directly.
     */
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
    external returns (uint256 validationData);
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
import {calldataKeccak} from "../core/Helpers.sol";
/**
 * User Operation struct
 * @param sender the sender account of this request.
     * @param nonce unique value the sender uses to verify it is not a replay.
     * @param initCode if set, the account contract will be created by this constructor/
     * @param callData the method call to execute on this account.
     * @param callGasLimit the gas limit passed to the callData method call.
     * @param verificationGasLimit gas used for validateUserOp and validatePaymasterUserOp.
     * @param preVerificationGas gas not calculated by the handleOps method, but added to the gas paid. Covers batch overhead.
     * @param maxFeePerGas same as EIP-1559 gas parameter.
     * @param maxPriorityFeePerGas same as EIP-1559 gas parameter.
     * @param paymasterAndData if set, this field holds the paymaster address and paymaster-specific data. the paymaster will pay for the transaction instead of the sender.
     * @param signature sender-verified signature over the entire request, the EntryPoint address and the chain ID.
     */
    struct UserOperation {
        address sender;
        uint256 nonce;
        bytes initCode;
        bytes callData;
        uint256 callGasLimit;
        uint256 verificationGasLimit;
        uint256 preVerificationGas;
        uint256 maxFeePerGas;
        uint256 maxPriorityFeePerGas;
        bytes paymasterAndData;
        bytes signature;
    }
/**
 * Utility functions helpful when working with UserOperation structs.
 */
library UserOperationLib {
    function getSender(UserOperation calldata userOp) internal pure returns (address) {
        address data;
        //read sender from userOp, which is first userOp member (saves 800 gas...)
        assembly {data := calldataload(userOp)}
        return address(uint160(data));
    }
    //relayer/block builder might submit the TX with higher priorityFee, but the user should not
    // pay above what he signed for.
    function gasPrice(UserOperation calldata userOp) internal view returns (uint256) {
    unchecked {
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        if (maxFeePerGas == maxPriorityFeePerGas) {
            //legacy mode (for networks that don't support basefee opcode)
            return maxFeePerGas;
        }
        return min(maxFeePerGas, maxPriorityFeePerGas + block.basefee);
    }
    }
    function pack(UserOperation calldata userOp) internal pure returns (bytes memory ret) {
        address sender = getSender(userOp);
        uint256 nonce = userOp.nonce;
        bytes32 hashInitCode = calldataKeccak(userOp.initCode);
        bytes32 hashCallData = calldataKeccak(userOp.callData);
        uint256 callGasLimit = userOp.callGasLimit;
        uint256 verificationGasLimit = userOp.verificationGasLimit;
        uint256 preVerificationGas = userOp.preVerificationGas;
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        bytes32 hashPaymasterAndData = calldataKeccak(userOp.paymasterAndData);
        return abi.encode(
            sender, nonce,
            hashInitCode, hashCallData,
            callGasLimit, verificationGasLimit, preVerificationGas,
            maxFeePerGas, maxPriorityFeePerGas,
            hashPaymasterAndData
        );
    }
    function hash(UserOperation calldata userOp) internal pure returns (bytes32) {
        return keccak256(pack(userOp));
    }
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Receiver mixin for ETH and safe-transferred ERC721 and ERC1155 tokens.
/// @author Solady (https://github.com/Vectorized/solady/blob/main/src/accounts/Receiver.sol)
///
/// @dev Note:
/// - Handles all ERC721 and ERC1155 token safety callbacks.
/// - Collapses function table gas overhead and code size.
/// - Utilizes fallback so unknown calldata will pass on.
abstract contract Receiver {
    /// @dev For receiving ETH.
    receive() external payable virtual {}
    /// @dev Fallback function with the `receiverFallback` modifier.
    fallback() external payable virtual receiverFallback {}
    /// @dev Modifier for the fallback function to handle token callbacks.
    modifier receiverFallback() virtual {
        /// @solidity memory-safe-assembly
        assembly {
            let s := shr(224, calldataload(0))
            // 0x150b7a02: `onERC721Received(address,address,uint256,bytes)`.
            // 0xf23a6e61: `onERC1155Received(address,address,uint256,uint256,bytes)`.
            // 0xbc197c81: `onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)`.
            if or(eq(s, 0x150b7a02), or(eq(s, 0xf23a6e61), eq(s, 0xbc197c81))) {
                mstore(0x20, s) // Store `msg.sig`.
                return(0x3c, 0x20) // Return `msg.sig`.
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Signature verification helper that supports both ECDSA signatures from EOAs
/// and ERC1271 signatures from smart contract wallets like Argent and Gnosis safe.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SignatureCheckerLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/cryptography/SignatureChecker.sol)
///
/// @dev Note:
/// - The signature checking functions use the ecrecover precompile (0x1).
/// - The `bytes memory signature` variants use the identity precompile (0x4)
///   to copy memory internally.
/// - Unlike ECDSA signatures, contract signatures are revocable.
/// - As of Solady version 0.0.134, all `bytes signature` variants accept both
///   regular 65-byte `(r, s, v)` and EIP-2098 `(r, vs)` short form signatures.
///   See: https://eips.ethereum.org/EIPS/eip-2098
///   This is for calldata efficiency on smart accounts prevalent on L2s.
///
/// WARNING! Do NOT use signatures as unique identifiers:
/// - Use a nonce in the digest to prevent replay attacks on the same contract.
/// - Use EIP-712 for the digest to prevent replay attacks across different chains and contracts.
///   EIP-712 also enables readable signing of typed data for better user safety.
/// This implementation does NOT check if a signature is non-malleable.
library SignatureCheckerLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*               SIGNATURE CHECKING OPERATIONS                */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x40, mload(add(signature, 0x20))) // `r`.
                if eq(mload(signature), 64) {
                    let vs := mload(add(signature, 0x40))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(mload(signature), 65) {
                    mstore(0x20, byte(0, mload(add(signature, 0x60)))) // `v`.
                    mstore(0x60, mload(add(signature, 0x40))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                // Copy the `signature` over.
                let n := add(0x20, mload(signature))
                pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(returndatasize(), 0x44), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNowCalldata(address signer, bytes32 hash, bytes calldata signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                if eq(signature.length, 64) {
                    let vs := calldataload(add(signature.offset, 0x20))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x40, calldataload(signature.offset)) // `r`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(signature.length, 65) {
                    mstore(0x20, byte(0, calldataload(add(signature.offset, 0x40)))) // `v`.
                    calldatacopy(0x40, signature.offset, 0x40) // `r`, `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), signature.length)
                // Copy the `signature` over.
                calldatacopy(add(m, 0x64), signature.offset, signature.length)
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(signature.length, 0x64), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, add(shr(255, vs), 27)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, shr(1, shl(1, vs))) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), mload(0x60)) // `s`.
                mstore8(add(m, 0xa4), mload(0x20)) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, and(v, 0xff)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, s) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), s) // `s`.
                mstore8(add(m, 0xa4), v) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     ERC1271 OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            // Copy the `signature` over.
            let n := add(0x20, mload(signature))
            pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(returndatasize(), 0x44), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNowCalldata(
        address signer,
        bytes32 hash,
        bytes calldata signature
    ) internal view returns (bool isValid) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), signature.length)
            // Copy the `signature` over.
            calldatacopy(add(m, 0x64), signature.offset, signature.length)
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(signature.length, 0x64), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), shr(1, shl(1, vs))) // `s`.
            mstore8(add(m, 0xa4), add(shr(255, vs), 27)) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), s) // `s`.
            mstore8(add(m, 0xa4), v) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     HASHING OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an Ethereum Signed Message, created from a `hash`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, hash) // Store into scratch space for keccak256.
            mstore(0x00, "\\x00\\x00\\x00\\x00\\x19Ethereum Signed Message:\
32") // 28 bytes.
            result := keccak256(0x04, 0x3c) // `32 * 2 - (32 - 28) = 60 = 0x3c`.
        }
    }
    /// @dev Returns an Ethereum Signed Message, created from `s`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    /// Note: Supports lengths of `s` up to 999999 bytes.
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let sLength := mload(s)
            let o := 0x20
            mstore(o, "\\x19Ethereum Signed Message:\
") // 26 bytes, zero-right-padded.
            mstore(0x00, 0x00)
            // Convert the `s.length` to ASCII decimal representation: `base10(s.length)`.
            for { let temp := sLength } 1 {} {
                o := sub(o, 1)
                mstore8(o, add(48, mod(temp, 10)))
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let n := sub(0x3a, o) // Header length: `26 + 32 - o`.
            // Throw an out-of-offset error (consumes all gas) if the header exceeds 32 bytes.
            returndatacopy(returndatasize(), returndatasize(), gt(n, 0x20))
            mstore(s, or(mload(0x00), mload(n))) // Temporarily store the header.
            result := keccak256(add(s, sub(0x20, n)), add(n, sLength))
            mstore(s, sLength) // Restore the length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   EMPTY CALLDATA HELPERS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an empty calldata bytes.
    function emptySignature() internal pure returns (bytes calldata signature) {
        /// @solidity memory-safe-assembly
        assembly {
            signature.length := 0
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice UUPS proxy mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/UUPSUpgradeable.sol)
/// @author Modified from OpenZeppelin
/// (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/proxy/utils/UUPSUpgradeable.sol)
///
/// Note:
/// - This implementation is intended to be used with ERC1967 proxies.
/// See: `LibClone.deployERC1967` and related functions.
/// - This implementation is NOT compatible with legacy OpenZeppelin proxies
/// which do not store the implementation at `_ERC1967_IMPLEMENTATION_SLOT`.
abstract contract UUPSUpgradeable {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The upgrade failed.
    error UpgradeFailed();
    /// @dev The call is from an unauthorized call context.
    error UnauthorizedCallContext();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         IMMUTABLES                         */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev For checking if the context is a delegate call.
    uint256 private immutable __self = uint256(uint160(address(this)));
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           EVENTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Emitted when the proxy's implementation is upgraded.
    event Upgraded(address indexed implementation);
    /// @dev `keccak256(bytes("Upgraded(address)"))`.
    uint256 private constant _UPGRADED_EVENT_SIGNATURE =
        0xbc7cd75a20ee27fd9adebab32041f755214dbc6bffa90cc0225b39da2e5c2d3b;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STORAGE                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The ERC-1967 storage slot for the implementation in the proxy.
    /// `uint256(keccak256("eip1967.proxy.implementation")) - 1`.
    bytes32 internal constant _ERC1967_IMPLEMENTATION_SLOT =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      UUPS OPERATIONS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Please override this function to check if `msg.sender` is authorized
    /// to upgrade the proxy to `newImplementation`, reverting if not.
    /// ```
    ///     function _authorizeUpgrade(address) internal override onlyOwner {}
    /// ```
    function _authorizeUpgrade(address newImplementation) internal virtual;
    /// @dev Returns the storage slot used by the implementation,
    /// as specified in [ERC1822](https://eips.ethereum.org/EIPS/eip-1822).
    ///
    /// Note: The `notDelegated` modifier prevents accidental upgrades to
    /// an implementation that is a proxy contract.
    function proxiableUUID() public view virtual notDelegated returns (bytes32) {
        // This function must always return `_ERC1967_IMPLEMENTATION_SLOT` to comply with ERC1967.
        return _ERC1967_IMPLEMENTATION_SLOT;
    }
    /// @dev Upgrades the proxy's implementation to `newImplementation`.
    /// Emits a {Upgraded} event.
    ///
    /// Note: Passing in empty `data` skips the delegatecall to `newImplementation`.
    function upgradeToAndCall(address newImplementation, bytes calldata data)
        public
        payable
        virtual
        onlyProxy
    {
        _authorizeUpgrade(newImplementation);
        /// @solidity memory-safe-assembly
        assembly {
            newImplementation := shr(96, shl(96, newImplementation)) // Clears upper 96 bits.
            mstore(0x01, 0x52d1902d) // `proxiableUUID()`.
            let s := _ERC1967_IMPLEMENTATION_SLOT
            // Check if `newImplementation` implements `proxiableUUID` correctly.
            if iszero(eq(mload(staticcall(gas(), newImplementation, 0x1d, 0x04, 0x01, 0x20)), s)) {
                mstore(0x01, 0x55299b49) // `UpgradeFailed()`.
                revert(0x1d, 0x04)
            }
            // Emit the {Upgraded} event.
            log2(codesize(), 0x00, _UPGRADED_EVENT_SIGNATURE, newImplementation)
            sstore(s, newImplementation) // Updates the implementation.
            // Perform a delegatecall to `newImplementation` if `data` is non-empty.
            if data.length {
                // Forwards the `data` to `newImplementation` via delegatecall.
                let m := mload(0x40)
                calldatacopy(m, data.offset, data.length)
                if iszero(delegatecall(gas(), newImplementation, m, data.length, codesize(), 0x00))
                {
                    // Bubble up the revert if the call reverts.
                    returndatacopy(m, 0x00, returndatasize())
                    revert(m, returndatasize())
                }
            }
        }
    }
    /// @dev Requires that the execution is performed through a proxy.
    modifier onlyProxy() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            // To enable use cases with an immutable default implementation in the bytecode,
            // (see: ERC6551Proxy), we don't require that the proxy address must match the
            // value stored in the implementation slot, which may not be initialized.
            if eq(s, address()) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
    /// @dev Requires that the execution is NOT performed via delegatecall.
    /// This is the opposite of `onlyProxy`.
    modifier notDelegated() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(eq(s, address())) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import {FCL_ecdsa} from "FreshCryptoLib/FCL_ecdsa.sol";
import {FCL_Elliptic_ZZ} from "FreshCryptoLib/FCL_elliptic.sol";
import {Base64} from "openzeppelin-contracts/contracts/utils/Base64.sol";
import {LibString} from "solady/utils/LibString.sol";
/// @title WebAuthn
///
/// @notice A library for verifying WebAuthn Authentication Assertions, built off the work
///         of Daimo.
///
/// @dev Attempts to use the RIP-7212 precompile for signature verification.
///      If precompile verification fails, it falls back to FreshCryptoLib.
///
/// @author Coinbase (https://github.com/base-org/webauthn-sol)
/// @author Daimo (https://github.com/daimo-eth/p256-verifier/blob/master/src/WebAuthn.sol)
library WebAuthn {
    using LibString for string;
    struct WebAuthnAuth {
        /// @dev The WebAuthn authenticator data.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorassertionresponse-authenticatordata.
        bytes authenticatorData;
        /// @dev The WebAuthn client data JSON.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorresponse-clientdatajson.
        string clientDataJSON;
        /// @dev The index at which "challenge":"..." occurs in `clientDataJSON`.
        uint256 challengeIndex;
        /// @dev The index at which "type":"..." occurs in `clientDataJSON`.
        uint256 typeIndex;
        /// @dev The r value of secp256r1 signature
        uint256 r;
        /// @dev The s value of secp256r1 signature
        uint256 s;
    }
    /// @dev Bit 0 of the authenticator data struct, corresponding to the "User Present" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UP = 0x01;
    /// @dev Bit 2 of the authenticator data struct, corresponding to the "User Verified" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UV = 0x04;
    /// @dev Secp256r1 curve order / 2 used as guard to prevent signature malleability issue.
    uint256 private constant _P256_N_DIV_2 = FCL_Elliptic_ZZ.n / 2;
    /// @dev The precompiled contract address to use for signature verification in the “secp256r1” elliptic curve.
    ///      See https://github.com/ethereum/RIPs/blob/master/RIPS/rip-7212.md.
    address private constant _VERIFIER = address(0x100);
    /// @dev The expected type (hash) in the client data JSON when verifying assertion signatures.
    ///      See https://www.w3.org/TR/webauthn-2/#dom-collectedclientdata-type
    bytes32 private constant _EXPECTED_TYPE_HASH = keccak256('"type":"webauthn.get"');
    ///
    /// @notice Verifies a Webauthn Authentication Assertion as described
    /// in https://www.w3.org/TR/webauthn-2/#sctn-verifying-assertion.
    ///
    /// @dev We do not verify all the steps as described in the specification, only ones relevant to our context.
    ///      Please carefully read through this list before usage.
    ///
    ///      Specifically, we do verify the following:
    ///         - Verify that authenticatorData (which comes from the authenticator, such as iCloud Keychain) indicates
    ///           a well-formed assertion with the user present bit set. If `requireUV` is set, checks that the authenticator
    ///           enforced user verification. User verification should be required if, and only if, options.userVerification
    ///           is set to required in the request.
    ///         - Verifies that the client JSON is of type "webauthn.get", i.e. the client was responding to a request to
    ///           assert authentication.
    ///         - Verifies that the client JSON contains the requested challenge.
    ///         - Verifies that (r, s) constitute a valid signature over both the authenicatorData and client JSON, for public
    ///            key (x, y).
    ///
    ///      We make some assumptions about the particular use case of this verifier, so we do NOT verify the following:
    ///         - Does NOT verify that the origin in the `clientDataJSON` matches the Relying Party's origin: tt is considered
    ///           the authenticator's responsibility to ensure that the user is interacting with the correct RP. This is
    ///           enforced by most high quality authenticators properly, particularly the iCloud Keychain and Google Password
    ///           Manager were tested.
    ///         - Does NOT verify That `topOrigin` in `clientDataJSON` is well-formed: We assume it would never be present, i.e.
    ///           the credentials are never used in a cross-origin/iframe context. The website/app set up should disallow
    ///           cross-origin usage of the credentials. This is the default behaviour for created credentials in common settings.
    ///         - Does NOT verify that the `rpIdHash` in `authenticatorData` is the SHA-256 hash of the RP ID expected by the Relying
    ///           Party: this means that we rely on the authenticator to properly enforce credentials to be used only by the correct RP.
    ///           This is generally enforced with features like Apple App Site Association and Google Asset Links. To protect from
    ///           edge cases in which a previously-linked RP ID is removed from the authorised RP IDs, we recommend that messages
    ///           signed by the authenticator include some expiry mechanism.
    ///         - Does NOT verify the credential backup state: this assumes the credential backup state is NOT used as part of Relying
    ///           Party business logic or policy.
    ///         - Does NOT verify the values of the client extension outputs: this assumes that the Relying Party does not use client
    ///           extension outputs.
    ///         - Does NOT verify the signature counter: signature counters are intended to enable risk scoring for the Relying Party.
    ///           This assumes risk scoring is not used as part of Relying Party business logic or policy.
    ///         - Does NOT verify the attestation object: this assumes that response.attestationObject is NOT present in the response,
    ///           i.e. the RP does not intend to verify an attestation.
    ///
    /// @param challenge    The challenge that was provided by the relying party.
    /// @param requireUV    A boolean indicating whether user verification is required.
    /// @param webAuthnAuth The `WebAuthnAuth` struct.
    /// @param x            The x coordinate of the public key.
    /// @param y            The y coordinate of the public key.
    ///
    /// @return `true` if the authentication assertion passed validation, else `false`.
    function verify(bytes memory challenge, bool requireUV, WebAuthnAuth memory webAuthnAuth, uint256 x, uint256 y)
        internal
        view
        returns (bool)
    {
        if (webAuthnAuth.s > _P256_N_DIV_2) {
            // guard against signature malleability
            return false;
        }
        // 11. Verify that the value of C.type is the string webauthn.get.
        //     bytes("type":"webauthn.get").length = 21
        string memory _type = webAuthnAuth.clientDataJSON.slice(webAuthnAuth.typeIndex, webAuthnAuth.typeIndex + 21);
        if (keccak256(bytes(_type)) != _EXPECTED_TYPE_HASH) {
            return false;
        }
        // 12. Verify that the value of C.challenge equals the base64url encoding of options.challenge.
        bytes memory expectedChallenge = bytes(string.concat('"challenge":"', Base64.encodeURL(challenge), '"'));
        string memory actualChallenge =
            webAuthnAuth.clientDataJSON.slice(webAuthnAuth.challengeIndex, webAuthnAuth.challengeIndex + expectedChallenge.length);
        if (keccak256(bytes(actualChallenge)) != keccak256(expectedChallenge)) {
            return false;
        }
        // Skip 13., 14., 15.
        // 16. Verify that the UP bit of the flags in authData is set.
        if (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UP != _AUTH_DATA_FLAGS_UP) {
            return false;
        }
        // 17. If user verification is required for this assertion, verify that the User Verified bit of the flags in
        //     authData is set.
        if (requireUV && (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UV) != _AUTH_DATA_FLAGS_UV) {
            return false;
        }
        // skip 18.
        // 19. Let hash be the result of computing a hash over the cData using SHA-256.
        bytes32 clientDataJSONHash = sha256(bytes(webAuthnAuth.clientDataJSON));
        // 20. Using credentialPublicKey, verify that sig is a valid signature over the binary concatenation of authData
        //     and hash.
        bytes32 messageHash = sha256(abi.encodePacked(webAuthnAuth.authenticatorData, clientDataJSONHash));
        bytes memory args = abi.encode(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
        // try the RIP-7212 precompile address
        (bool success, bytes memory ret) = _VERIFIER.staticcall(args);
        // staticcall will not revert if address has no code
        // check return length
        // note that even if precompile exists, ret.length is 0 when verification returns false
        // so an invalid signature will be checked twice: once by the precompile and once by FCL.
        // Ideally this signature failure is simulated offchain and no one actually pay this gas.
        bool valid = ret.length > 0;
        if (success && valid) return abi.decode(ret, (uint256)) == 1;
        return FCL_ecdsa.ecdsa_verify(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @title ERC-1271
///
/// @notice Abstract ERC-1271 implementation (based on Solady's) with guards to handle the same
///         signer being used on multiple accounts.
///
/// @dev To prevent the same signature from being validated on different accounts owned by the samer signer,
///      we introduce an anti cross-account-replay layer: the original hash is input into a new EIP-712 compliant
///      hash. The domain separator of this outer hash contains the chain id and address of this contract, so that
///      it cannot be used on two accounts (see `replaySafeHash()` for the implementation details).
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC1271.sol)
abstract contract ERC1271 {
    /// @dev Precomputed `typeHash` used to produce EIP-712 compliant hash when applying the anti
    ///      cross-account-replay layer.
    ///
    ///      The original hash must either be:
    ///         - An EIP-191 hash: keccak256("\\x19Ethereum Signed Message:\
" || len(someMessage) || someMessage)
    ///         - An EIP-712 hash: keccak256("\\x19\\x01" || someDomainSeparator || hashStruct(someStruct))
    bytes32 private constant _MESSAGE_TYPEHASH = keccak256("CoinbaseSmartWalletMessage(bytes32 hash)");
    /// @notice Returns information about the `EIP712Domain` used to create EIP-712 compliant hashes.
    ///
    /// @dev Follows ERC-5267 (see https://eips.ethereum.org/EIPS/eip-5267).
    ///
    /// @return fields The bitmap of used fields.
    /// @return name The value of the `EIP712Domain.name` field.
    /// @return version The value of the `EIP712Domain.version` field.
    /// @return chainId The value of the `EIP712Domain.chainId` field.
    /// @return verifyingContract The value of the `EIP712Domain.verifyingContract` field.
    /// @return salt The value of the `EIP712Domain.salt` field.
    /// @return extensions The list of EIP numbers, that extends EIP-712 with new domain fields.
    function eip712Domain()
        external
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        fields = hex"0f"; // `0b1111`.
        (name, version) = _domainNameAndVersion();
        chainId = block.chainid;
        verifyingContract = address(this);
        salt = salt; // `bytes32(0)`.
        extensions = extensions; // `new uint256[](0)`.
    }
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev This implementation follows ERC-1271. See https://eips.ethereum.org/EIPS/eip-1271.
    /// @dev IMPORTANT: Signature verification is performed on the hash produced AFTER applying the anti
    ///      cross-account-replay layer on the given `hash` (i.e., verification is run on the replay-safe
    ///      hash version).
    ///
    /// @param hash      The original hash.
    /// @param signature The signature of the replay-safe hash to validate.
    ///
    /// @return result `0x1626ba7e` if validation succeeded, else `0xffffffff`.
    function isValidSignature(bytes32 hash, bytes calldata signature) public view virtual returns (bytes4 result) {
        if (_isValidSignature({hash: replaySafeHash(hash), signature: signature})) {
            // bytes4(keccak256("isValidSignature(bytes32,bytes)"))
            return 0x1626ba7e;
        }
        return 0xffffffff;
    }
    /// @notice Wrapper around `_eip712Hash()` to produce a replay-safe hash fron the given `hash`.
    ///
    /// @dev The returned EIP-712 compliant replay-safe hash is the result of:
    ///      keccak256(
    ///         \\x19\\x01 ||
    ///         this.domainSeparator ||
    ///         hashStruct(CoinbaseSmartWalletMessage({ hash: `hash`}))
    ///      )
    ///
    /// @param hash The original hash.
    ///
    /// @return The corresponding replay-safe hash.
    function replaySafeHash(bytes32 hash) public view virtual returns (bytes32) {
        return _eip712Hash(hash);
    }
    /// @notice Returns the `domainSeparator` used to create EIP-712 compliant hashes.
    ///
    /// @dev Implements domainSeparator = hashStruct(eip712Domain).
    ///      See https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator.
    ///
    /// @return The 32 bytes domain separator result.
    function domainSeparator() public view returns (bytes32) {
        (string memory name, string memory version) = _domainNameAndVersion();
        return keccak256(
            abi.encode(
                keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                keccak256(bytes(name)),
                keccak256(bytes(version)),
                block.chainid,
                address(this)
            )
        );
    }
    /// @notice Returns the EIP-712 typed hash of the `CoinbaseSmartWalletMessage(bytes32 hash)` data structure.
    ///
    /// @dev Implements encode(domainSeparator : 𝔹²⁵⁶, message : 𝕊) = "\\x19\\x01" || domainSeparator ||
    ///      hashStruct(message).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#specification.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field to hash.
    ////
    /// @return The resulting EIP-712 hash.
    function _eip712Hash(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encodePacked("\\x19\\x01", domainSeparator(), _hashStruct(hash)));
    }
    /// @notice Returns the EIP-712 `hashStruct` result of the `CoinbaseSmartWalletMessage(bytes32 hash)` data
    ///         structure.
    ///
    /// @dev Implements hashStruct(s : 𝕊) = keccak256(typeHash || encodeData(s)).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field.
    ///
    /// @return The EIP-712 `hashStruct` result.
    function _hashStruct(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encode(_MESSAGE_TYPEHASH, hash));
    }
    /// @notice Returns the domain name and version to use when creating EIP-712 signatures.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @return name    The user readable name of signing domain.
    /// @return version The current major version of the signing domain.
    function _domainNameAndVersion() internal view virtual returns (string memory name, string memory version);
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @param hash      The hash whose signature has been performed on.
    /// @param signature The signature associated with `hash`.
    ///
    /// @return `true` is the signature is valid, else `false`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.18;
/// @notice Storage layout used by this contract.
///
/// @custom:storage-location erc7201:coinbase.storage.MultiOwnable
struct MultiOwnableStorage {
    /// @dev Tracks the index of the next owner to add.
    uint256 nextOwnerIndex;
    /// @dev Tracks number of owners that have been removed.
    uint256 removedOwnersCount;
    /// @dev Maps index to owner bytes, used to idenfitied owners via a uint256 index.
    ///
    ///      Some uses—-such as signature validation for secp256r1 public key owners—-
    ///      requires the caller to assert the public key of the caller. To economize calldata,
    ///      we allow an index to identify an owner, so that the full owner bytes do
    ///      not need to be passed.
    ///
    ///      The `owner` bytes should either be
    ///         - An ABI encoded Ethereum address
    ///         - An ABI encoded public key
    mapping(uint256 index => bytes owner) ownerAtIndex;
    /// @dev Mapping of bytes to booleans indicating whether or not
    ///      bytes_ is an owner of this contract.
    mapping(bytes bytes_ => bool isOwner_) isOwner;
}
/// @title Multi Ownable
///
/// @notice Auth contract allowing multiple owners, each identified as bytes.
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
contract MultiOwnable {
    /// @dev Slot for the `MultiOwnableStorage` struct in storage.
    ///      Computed from
    ///      keccak256(abi.encode(uint256(keccak256("coinbase.storage.MultiOwnable")) - 1)) & ~bytes32(uint256(0xff))
    ///      Follows ERC-7201 (see https://eips.ethereum.org/EIPS/eip-7201).
    bytes32 private constant MUTLI_OWNABLE_STORAGE_LOCATION =
        0x97e2c6aad4ce5d562ebfaa00db6b9e0fb66ea5d8162ed5b243f51a2e03086f00;
    /// @notice Thrown when the `msg.sender` is not an owner and is trying to call a privileged function.
    error Unauthorized();
    /// @notice Thrown when trying to add an already registered owner.
    ///
    /// @param owner The owner bytes.
    error AlreadyOwner(bytes owner);
    /// @notice Thrown when trying to remove an owner from an index that is empty.
    ///
    /// @param index The targeted index for removal.
    error NoOwnerAtIndex(uint256 index);
    /// @notice Thrown when `owner` argument does not match owner found at index.
    ///
    /// @param index         The index of the owner to be removed.
    /// @param expectedOwner The owner passed in the remove call.
    /// @param actualOwner   The actual owner at `index`.
    error WrongOwnerAtIndex(uint256 index, bytes expectedOwner, bytes actualOwner);
    /// @notice Thrown when a provided owner is neither 64 bytes long (for public key)
    ///         nor a ABI encoded address.
    ///
    /// @param owner The invalid owner.
    error InvalidOwnerBytesLength(bytes owner);
    /// @notice Thrown if a provided owner is 32 bytes long but does not fit in an `address` type.
    ///
    /// @param owner The invalid owner.
    error InvalidEthereumAddressOwner(bytes owner);
    /// @notice Thrown when removeOwnerAtIndex is called and there is only one current owner.
    error LastOwner();
    /// @notice Thrown when removeLastOwner is called and there is more than one current owner.
    ///
    /// @param ownersRemaining The number of current owners.
    error NotLastOwner(uint256 ownersRemaining);
    /// @notice Emitted when a new owner is registered.
    ///
    /// @param index The owner index of the owner added.
    /// @param owner The owner added.
    event AddOwner(uint256 indexed index, bytes owner);
    /// @notice Emitted when an owner is removed.
    ///
    /// @param index The owner index of the owner removed.
    /// @param owner The owner removed.
    event RemoveOwner(uint256 indexed index, bytes owner);
    /// @notice Access control modifier ensuring the caller is an authorized owner
    modifier onlyOwner() virtual {
        _checkOwner();
        _;
    }
    /// @notice Adds a new Ethereum-address owner.
    ///
    /// @param owner The owner address.
    function addOwnerAddress(address owner) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(owner), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Adds a new public-key owner.
    ///
    /// @param x The owner public key x coordinate.
    /// @param y The owner public key y coordinate.
    function addOwnerPublicKey(bytes32 x, bytes32 y) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(x, y), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently only one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeOwnerAtIndex(uint256 index, bytes calldata owner) external virtual onlyOwner {
        if (ownerCount() == 1) {
            revert LastOwner();
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Removes owner at the given `index`, which should be the only current owner.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently more than one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeLastOwner(uint256 index, bytes calldata owner) external virtual onlyOwner {
        uint256 ownersRemaining = ownerCount();
        if (ownersRemaining > 1) {
            revert NotLastOwner(ownersRemaining);
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Checks if the given `account` address is registered as owner.
    ///
    /// @param account The account address to check.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerAddress(address account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(account)];
    }
    /// @notice Checks if the given `x`, `y` public key is registered as owner.
    ///
    /// @param x The public key x coordinate.
    /// @param y The public key y coordinate.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerPublicKey(bytes32 x, bytes32 y) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(x, y)];
    }
    /// @notice Checks if the given `account` bytes is registered as owner.
    ///
    /// @param account The account, should be ABI encoded address or public key.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerBytes(bytes memory account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[account];
    }
    /// @notice Returns the owner bytes at the given `index`.
    ///
    /// @param index The index to lookup.
    ///
    /// @return The owner bytes (empty if no owner is registered at this `index`).
    function ownerAtIndex(uint256 index) public view virtual returns (bytes memory) {
        return _getMultiOwnableStorage().ownerAtIndex[index];
    }
    /// @notice Returns the next index that will be used to add a new owner.
    ///
    /// @return The next index that will be used to add a new owner.
    function nextOwnerIndex() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().nextOwnerIndex;
    }
    /// @notice Returns the current number of owners
    ///
    /// @return The current owner count
    function ownerCount() public view virtual returns (uint256) {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        return $.nextOwnerIndex - $.removedOwnersCount;
    }
    /// @notice Tracks the number of owners removed
    ///
    /// @dev Used with `this.nextOwnerIndex` to avoid removing all owners
    ///
    /// @return The number of owners that have been removed.
    function removedOwnersCount() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().removedOwnersCount;
    }
    /// @notice Initialize the owners of this contract.
    ///
    /// @dev Intended to be called contract is first deployed and never again.
    /// @dev Reverts if a provided owner is neither 64 bytes long (for public key) nor a valid address.
    ///
    /// @param owners The initial set of owners.
    function _initializeOwners(bytes[] memory owners) internal virtual {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        uint256 nextOwnerIndex_ = $.nextOwnerIndex;
        for (uint256 i; i < owners.length; i++) {
            if (owners[i].length != 32 && owners[i].length != 64) {
                revert InvalidOwnerBytesLength(owners[i]);
            }
            if (owners[i].length == 32 && uint256(bytes32(owners[i])) > type(uint160).max) {
                revert InvalidEthereumAddressOwner(owners[i]);
            }
            _addOwnerAtIndex(owners[i], nextOwnerIndex_++);
        }
        $.nextOwnerIndex = nextOwnerIndex_;
    }
    /// @notice Adds an owner at the given `index`.
    ///
    /// @dev Reverts if `owner` is already registered as an owner.
    ///
    /// @param owner The owner raw bytes to register.
    /// @param index The index to write to.
    function _addOwnerAtIndex(bytes memory owner, uint256 index) internal virtual {
        if (isOwnerBytes(owner)) revert AlreadyOwner(owner);
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        $.isOwner[owner] = true;
        $.ownerAtIndex[index] = owner;
        emit AddOwner(index, owner);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function _removeOwnerAtIndex(uint256 index, bytes calldata owner) internal virtual {
        bytes memory owner_ = ownerAtIndex(index);
        if (owner_.length == 0) revert NoOwnerAtIndex(index);
        if (keccak256(owner_) != keccak256(owner)) {
            revert WrongOwnerAtIndex({index: index, expectedOwner: owner, actualOwner: owner_});
        }
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        delete $.isOwner[owner];
        delete $.ownerAtIndex[index];
        $.removedOwnersCount++;
        emit RemoveOwner(index, owner);
    }
    /// @notice Checks if the sender is an owner of this contract or the contract itself.
    ///
    /// @dev Revert if the sender is not an owner fo the contract itself.
    function _checkOwner() internal view virtual {
        if (isOwnerAddress(msg.sender) || (msg.sender == address(this))) {
            return;
        }
        revert Unauthorized();
    }
    /// @notice Helper function to get a storage reference to the `MultiOwnableStorage` struct.
    ///
    /// @return $ A storage reference to the `MultiOwnableStorage` struct.
    function _getMultiOwnableStorage() internal pure returns (MultiOwnableStorage storage $) {
        assembly ("memory-safe") {
            $.slot := MUTLI_OWNABLE_STORAGE_LOCATION
        }
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
/**
 * returned data from validateUserOp.
 * validateUserOp returns a uint256, with is created by `_packedValidationData` and parsed by `_parseValidationData`
 * @param aggregator - address(0) - the account validated the signature by itself.
 *              address(1) - the account failed to validate the signature.
 *              otherwise - this is an address of a signature aggregator that must be used to validate the signature.
 * @param validAfter - this UserOp is valid only after this timestamp.
 * @param validaUntil - this UserOp is valid only up to this timestamp.
 */
    struct ValidationData {
        address aggregator;
        uint48 validAfter;
        uint48 validUntil;
    }
//extract sigFailed, validAfter, validUntil.
// also convert zero validUntil to type(uint48).max
    function _parseValidationData(uint validationData) pure returns (ValidationData memory data) {
        address aggregator = address(uint160(validationData));
        uint48 validUntil = uint48(validationData >> 160);
        if (validUntil == 0) {
            validUntil = type(uint48).max;
        }
        uint48 validAfter = uint48(validationData >> (48 + 160));
        return ValidationData(aggregator, validAfter, validUntil);
    }
// intersect account and paymaster ranges.
    function _intersectTimeRange(uint256 validationData, uint256 paymasterValidationData) pure returns (ValidationData memory) {
        ValidationData memory accountValidationData = _parseValidationData(validationData);
        ValidationData memory pmValidationData = _parseValidationData(paymasterValidationData);
        address aggregator = accountValidationData.aggregator;
        if (aggregator == address(0)) {
            aggregator = pmValidationData.aggregator;
        }
        uint48 validAfter = accountValidationData.validAfter;
        uint48 validUntil = accountValidationData.validUntil;
        uint48 pmValidAfter = pmValidationData.validAfter;
        uint48 pmValidUntil = pmValidationData.validUntil;
        if (validAfter < pmValidAfter) validAfter = pmValidAfter;
        if (validUntil > pmValidUntil) validUntil = pmValidUntil;
        return ValidationData(aggregator, validAfter, validUntil);
    }
/**
 * helper to pack the return value for validateUserOp
 * @param data - the ValidationData to pack
 */
    function _packValidationData(ValidationData memory data) pure returns (uint256) {
        return uint160(data.aggregator) | (uint256(data.validUntil) << 160) | (uint256(data.validAfter) << (160 + 48));
    }
/**
 * helper to pack the return value for validateUserOp, when not using an aggregator
 * @param sigFailed - true for signature failure, false for success
 * @param validUntil last timestamp this UserOperation is valid (or zero for infinite)
 * @param validAfter first timestamp this UserOperation is valid
 */
    function _packValidationData(bool sigFailed, uint48 validUntil, uint48 validAfter) pure returns (uint256) {
        return (sigFailed ? 1 : 0) | (uint256(validUntil) << 160) | (uint256(validAfter) << (160 + 48));
    }
/**
 * keccak function over calldata.
 * @dev copy calldata into memory, do keccak and drop allocated memory. Strangely, this is more efficient than letting solidity do it.
 */
    function calldataKeccak(bytes calldata data) pure returns (bytes32 ret) {
        assembly {
            let mem := mload(0x40)
            let len := data.length
            calldatacopy(mem, data.offset, len)
            ret := keccak256(mem, len)
        }
    }
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_ecdsa.sol
///*
///*
///* DESCRIPTION: ecdsa verification implementation
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
import {FCL_Elliptic_ZZ} from "./FCL_elliptic.sol";
library FCL_ecdsa {
    // Set parameters for curve sec256r1.public
      //curve order (number of points)
    uint256 constant n = FCL_Elliptic_ZZ.n;
  
    /**
     * @dev ECDSA verification, given , signature, and public key.
     */
    /**
     * @dev ECDSA verification, given , signature, and public key, no calldata version
     */
    function ecdsa_verify(bytes32 message, uint256 r, uint256 s, uint256 Qx, uint256 Qy)  internal view returns (bool){
        if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return false;
        }
        
        if (!FCL_Elliptic_ZZ.ecAff_isOnCurve(Qx, Qy)) {
            return false;
        }
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 scalar_u = mulmod(uint256(message), sInv, FCL_Elliptic_ZZ.n);
        uint256 scalar_v = mulmod(r, sInv, FCL_Elliptic_ZZ.n);
        uint256 x1;
        x1 = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S_asm(Qx, Qy, scalar_u, scalar_v);
        x1= addmod(x1, n-r,n );
    
        return x1 == 0;
    }
    function ec_recover_r1(uint256 h, uint256 v, uint256 r, uint256 s) internal view returns (address)
    {
         if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return address(0);
        }
        uint256 y=FCL_Elliptic_ZZ.ec_Decompress(r, v-27);
        uint256 rinv=FCL_Elliptic_ZZ.FCL_nModInv(r);
        uint256 u1=mulmod(FCL_Elliptic_ZZ.n-addmod(0,h,FCL_Elliptic_ZZ.n), rinv,FCL_Elliptic_ZZ.n);//-hr^-1
        uint256 u2=mulmod(s, rinv,FCL_Elliptic_ZZ.n);//sr^-1
        uint256 Qx;
        uint256 Qy;
        (Qx,Qy)=FCL_Elliptic_ZZ.ecZZ_mulmuladd(r,y, u1, u2);
        return address(uint160(uint256(keccak256(abi.encodePacked(Qx, Qy)))));
    }
    function ecdsa_precomputed_verify(bytes32 message, uint256 r, uint256 s, address Shamir8)
        internal view
        returns (bool)
    {
       
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
     function ecdsa_precomputed_verify(bytes32 message, uint256[2] calldata rs, address Shamir8)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
}
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_elliptic.sol
///*
///*
///* DESCRIPTION: modified XYZZ system coordinates for EVM elliptic point multiplication
///*  optimization
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
library FCL_Elliptic_ZZ {
    // Set parameters for curve sec256r1.
    // address of the ModExp precompiled contract (Arbitrary-precision exponentiation under modulo)
    address constant MODEXP_PRECOMPILE = 0x0000000000000000000000000000000000000005;
    //curve prime field modulus
    uint256 constant p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    //short weierstrass first coefficient
    uint256 constant a = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC;
    //short weierstrass second coefficient
    uint256 constant b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B;
    //generating point affine coordinates
    uint256 constant gx = 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296;
    uint256 constant gy = 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5;
    //curve order (number of points)
    uint256 constant n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551;
    /* -2 mod p constant, used to speed up inversion and doubling (avoid negation)*/
    uint256 constant minus_2 = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFD;
    /* -2 mod n constant, used to speed up inversion*/
    uint256 constant minus_2modn = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC63254F;
    uint256 constant minus_1 = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
    //P+1 div 4
    uint256 constant pp1div4=0x3fffffffc0000000400000000000000000000000400000000000000000000000;
    //arbitrary constant to express no quadratic residuosity
    uint256 constant _NOTSQUARE=0xFFFFFFFF00000002000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    uint256 constant _NOTONCURVE=0xFFFFFFFF00000003000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    /**
     * /* inversion mod n via a^(n-2), use of precompiled using little Fermat theorem
     */
    function FCL_nModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2modn)
            mstore(add(pointer, 0xa0), n)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    /**
     * /* @dev inversion mod nusing little Fermat theorem via a^(n-2), use of precompiled
     */
    function FCL_pModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2)
            mstore(add(pointer, 0xa0), p)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    //Coron projective shuffling, take as input alpha as blinding factor
   function ecZZ_Coronize(uint256 alpha, uint256 x, uint256 y,  uint256 zz, uint256 zzz) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
   {
       
        uint256 alpha2=mulmod(alpha,alpha,p);
       
        x3=mulmod(alpha2, x,p); //alpha^-2.x
        y3=mulmod(mulmod(alpha, alpha2,p), y,p);
        zz3=mulmod(zz,alpha2,p);//alpha^2 zz
        zzz3=mulmod(zzz,mulmod(alpha, alpha2,p),p);//alpha^3 zzz
        
        return (x3, y3, zz3, zzz3);
   }
 function ecZZ_Add(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2, uint256 zz2, uint256 zzz2) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
  {
    uint256 u1=mulmod(x1,zz2,p); // U1 = X1*ZZ2
    uint256 u2=mulmod(x2, zz1,p);               //  U2 = X2*ZZ1
    u2=addmod(u2, p-u1, p);//  P = U2-U1
    x1=mulmod(u2, u2, p);//PP
    x2=mulmod(x1, u2, p);//PPP
    
    zz3=mulmod(x1, mulmod(zz1, zz2, p),p);//ZZ3 = ZZ1*ZZ2*PP  
    zzz3=mulmod(zzz1, mulmod(zzz2, x2, p),p);//ZZZ3 = ZZZ1*ZZZ2*PPP
    zz1=mulmod(y1, zzz2,p);  // S1 = Y1*ZZZ2
    zz2=mulmod(y2, zzz1, p);    // S2 = Y2*ZZZ1 
    zz2=addmod(zz2, p-zz1, p);//R = S2-S1
    zzz1=mulmod(u1, x1,p); //Q = U1*PP
    x3= addmod(addmod(mulmod(zz2, zz2, p), p-x2,p), mulmod(minus_2, zzz1,p),p); //X3 = R2-PPP-2*Q
    y3=addmod( mulmod(zz2, addmod(zzz1, p-x3, p),p), p-mulmod(zz1, x2, p),p);//R*(Q-X3)-S1*PPP
    return (x3, y3, zz3, zzz3);
  }
/// @notice Calculate one modular square root of a given integer. Assume that p=3 mod 4.
/// @dev Uses the ModExp precompiled contract at address 0x05 for fast computation using little Fermat theorem
/// @param self The integer of which to find the modular inverse
/// @return result The modular inverse of the input integer. If the modular inverse doesn't exist, it revert the tx
function SqrtMod(uint256 self) internal view returns (uint256 result){
 assembly ("memory-safe") {
        // load the free memory pointer value
        let pointer := mload(0x40)
        // Define length of base (Bsize)
        mstore(pointer, 0x20)
        // Define the exponent size (Esize)
        mstore(add(pointer, 0x20), 0x20)
        // Define the modulus size (Msize)
        mstore(add(pointer, 0x40), 0x20)
        // Define variables base (B)
        mstore(add(pointer, 0x60), self)
        // Define the exponent (E)
        mstore(add(pointer, 0x80), pp1div4)
        // We save the point of the last argument, it will be override by the result
        // of the precompile call in order to avoid paying for the memory expansion properly
        let _result := add(pointer, 0xa0)
        // Define the modulus (M)
        mstore(_result, p)
        // Call the precompiled ModExp (0x05) https://www.evm.codes/precompiled#0x05
        if iszero(
            staticcall(
                not(0), // amount of gas to send
                MODEXP_PRECOMPILE, // target
                pointer, // argsOffset
                0xc0, // argsSize (6 * 32 bytes)
                _result, // retOffset (we override M to avoid paying for the memory expansion)
                0x20 // retSize (32 bytes)
            )
        ) { revert(0, 0) }
  result := mload(_result)
//  result :=addmod(result,0,p)
 }
   if(mulmod(result,result,p)!=self){
     result=_NOTSQUARE;
   }
  
   return result;
}
    /**
     * /* @dev Convert from affine rep to XYZZ rep
     */
    function ecAff_SetZZ(uint256 x0, uint256 y0) internal pure returns (uint256[4] memory P) {
        unchecked {
            P[2] = 1; //ZZ
            P[3] = 1; //ZZZ
            P[0] = x0;
            P[1] = y0;
        }
    }
    function ec_Decompress(uint256 x, uint256 parity) internal view returns(uint256 y){ 
        uint256 y2=mulmod(x,mulmod(x,x,p),p);//x3
        y2=addmod(b,addmod(y2,mulmod(x,a,p),p),p);//x3+ax+b
        y=SqrtMod(y2);
        if(y==_NOTSQUARE){
           return _NOTONCURVE;
        }
        if((y&1)!=(parity&1)){
            y=p-y;
        }
    }
    /**
     * /* @dev Convert from XYZZ rep to affine rep
     */
    /*    https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html#addition-add-2008-s*/
    function ecZZ_SetAff(uint256 x, uint256 y, uint256 zz, uint256 zzz) internal view returns (uint256 x1, uint256 y1) {
        uint256 zzzInv = FCL_pModInv(zzz); //1/zzz
        y1 = mulmod(y, zzzInv, p); //Y/zzz
        uint256 _b = mulmod(zz, zzzInv, p); //1/z
        zzzInv = mulmod(_b, _b, p); //1/zz
        x1 = mulmod(x, zzzInv, p); //X/zz
    }
    /**
     * /* @dev Sutherland2008 doubling
     */
    /* The "dbl-2008-s-1" doubling formulas */
    function ecZZ_Dbl(uint256 x, uint256 y, uint256 zz, uint256 zzz)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            assembly {
                P0 := mulmod(2, y, p) //U = 2*Y1
                P2 := mulmod(P0, P0, p) // V=U^2
                P3 := mulmod(x, P2, p) // S = X1*V
                P1 := mulmod(P0, P2, p) // W=UV
                P2 := mulmod(P2, zz, p) //zz3=V*ZZ1
                zz := mulmod(3, mulmod(addmod(x, sub(p, zz), p), addmod(x, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                P0 := addmod(mulmod(zz, zz, p), mulmod(minus_2, P3, p), p) //X3=M^2-2S
                x := mulmod(zz, addmod(P3, sub(p, P0), p), p) //M(S-X3)
                P3 := mulmod(P1, zzz, p) //zzz3=W*zzz1
                P1 := addmod(x, sub(p, mulmod(P1, y, p)), p) //Y3= M(S-X3)-W*Y1
            }
        }
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Sutherland2008 add a ZZ point with a normalized point and greedy formulae
     * warning: assume that P1(x1,y1)!=P2(x2,y2), true in multiplication loop with prime order (cofactor 1)
     */
    function ecZZ_AddN(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            if (y1 == 0) {
                return (x2, y2, 1, 1);
            }
            assembly {
                y1 := sub(p, y1)
                y2 := addmod(mulmod(y2, zzz1, p), y1, p)
                x2 := addmod(mulmod(x2, zz1, p), sub(p, x1), p)
                P0 := mulmod(x2, x2, p) //PP = P^2
                P1 := mulmod(P0, x2, p) //PPP = P*PP
                P2 := mulmod(zz1, P0, p) ////ZZ3 = ZZ1*PP
                P3 := mulmod(zzz1, P1, p) ////ZZZ3 = ZZZ1*PPP
                zz1 := mulmod(x1, P0, p) //Q = X1*PP
                P0 := addmod(addmod(mulmod(y2, y2, p), sub(p, P1), p), mulmod(minus_2, zz1, p), p) //R^2-PPP-2*Q
                P1 := addmod(mulmod(addmod(zz1, sub(p, P0), p), y2, p), mulmod(y1, P1, p), p) //R*(Q-X3)
            }
            //end assembly
        } //end unchecked
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Return the zero curve in XYZZ coordinates.
     */
    function ecZZ_SetZero() internal pure returns (uint256 x, uint256 y, uint256 zz, uint256 zzz) {
        return (0, 0, 0, 0);
    }
    /**
     * @dev Check if point is the neutral of the curve
     */
    // uint256 x0, uint256 y0, uint256 zz0, uint256 zzz0
    function ecZZ_IsZero(uint256, uint256 y0, uint256, uint256) internal pure returns (bool) {
        return y0 == 0;
    }
    /**
     * @dev Return the zero curve in affine coordinates. Compatible with the double formulae (no special case)
     */
    function ecAff_SetZero() internal pure returns (uint256 x, uint256 y) {
        return (0, 0);
    }
    /**
     * @dev Check if the curve is the zero curve in affine rep.
     */
    // uint256 x, uint256 y)
    function ecAff_IsZero(uint256, uint256 y) internal pure returns (bool flag) {
        return (y == 0);
    }
    /**
     * @dev Check if a point in affine coordinates is on the curve (reject Neutral that is indeed on the curve).
     */
    function ecAff_isOnCurve(uint256 x, uint256 y) internal pure returns (bool) {
        if (x >= p || y >= p || ((x == 0) && (y == 0))) {
            return false;
        }
        unchecked {
            uint256 LHS = mulmod(y, y, p); // y^2
            uint256 RHS = addmod(mulmod(mulmod(x, x, p), x, p), mulmod(x, a, p), p); // x^3+ax
            RHS = addmod(RHS, b, p); // x^3 + a*x + b
            return LHS == RHS;
        }
    }
    /**
     * @dev Add two elliptic curve points in affine coordinates. Deal with P=Q
     */
    function ecAff_add(uint256 x0, uint256 y0, uint256 x1, uint256 y1) internal view returns (uint256, uint256) {
        uint256 zz0;
        uint256 zzz0;
        if (ecAff_IsZero(x0, y0)) return (x1, y1);
        if (ecAff_IsZero(x1, y1)) return (x0, y0);
        if((x0==x1)&&(y0==y1)) {
            (x0, y0, zz0, zzz0) = ecZZ_Dbl(x0, y0,1,1);
        }
        else{
            (x0, y0, zz0, zzz0) = ecZZ_AddN(x0, y0, 1, 1, x1, y1);
        }
        return ecZZ_SetAff(x0, y0, zz0, zzz0);
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns only x for ECDSA use            
     *      */
    function ecZZ_mulmuladd_S_asm(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X) {
        uint256 zz;
        uint256 zzz;
        uint256 Y;
        uint256 index = 255;
        uint256 H0;
        uint256 H1;
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return 0;
            (H0, H1) = ecAff_add(gx, gy, Q0, Q1); 
            if((H0==0)&&(H1==0))//handling Q=-G
            {
                scalar_u=addmod(scalar_u, n-scalar_v, n);
                scalar_v=0;
                if (scalar_u == 0 && scalar_v == 0) return 0;
            }
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    X := H0
                    Y := H1
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := H0
                            T2 := H1
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                let T := mload(0x40)
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                //Y:=mulmod(Y,zzz,p)//Y/zzz
                //zz :=mulmod(zz, mload(T),p) //1/z
                //zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, mload(T), p) //X/zz
            } //end assembly
        } //end unchecked
        return X;
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns affine representation of point (normalized)       
     *      */
    function ecZZ_mulmuladd(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X, uint256 Y) {
        uint256 zz;
        uint256 zzz;
        uint256 index = 255;
        uint256[6] memory T;
        uint256[2] memory H;
 
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return (0,0);
            (H[0], H[1]) = ecAff_add(gx, gy, Q0, Q1); //will not work if Q=P, obvious forbidden private key
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    Y := mload(add(H,32))
                    X := mload(H)
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := mload(H)
                            T2 := mload(add(H,32))
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zzz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                Y:=mulmod(Y,mload(T),p)//Y/zzz
                zz :=mulmod(zz, mload(T),p) //1/z
                zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, zz, p) //X/zz
            } //end assembly
        } //end unchecked
        return (X,Y);
    }
    //8 dimensions Shamir's trick, using precomputations stored in Shamir8,  stored as Bytecode of an external
    //contract at given address dataPointer
    //(thx to Lakhdar https://github.com/Kelvyne for EVM storage explanations and tricks)
    // the external tool to generate tables from public key is in the /sage directory
    function ecZZ_mulmuladd_S8_extcode(uint256 scalar_u, uint256 scalar_v, address dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        unchecked {
            uint256 zz; // third and  coordinates of the point
            uint256[6] memory T;
            zz = 256; //start index
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                extcodecopy(dataPointer, T, mload(T), 64)
                let index := sub(zz, 1)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for {} gt(index, 191) { index := add(index, 191) } {
                    //inline Double
                    {
                        let TT1 := mulmod(2, Y, p) //U = 2*Y1, y free
                        let T2 := mulmod(TT1, TT1, p) // V=U^2
                        let T3 := mulmod(X, T2, p) // S = X1*V
                        let T1 := mulmod(TT1, T2, p) // W=UV
                        let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                        zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                        zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                        X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                        //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                        let T5 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                        //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                        Y := addmod(mulmod(T1, Y, p), T5, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                        /* compute element to access in precomputed table */
                    }
                    {
                        let T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                        let index2 := sub(index, 64)
                        let T3 :=
                            add(T4, add(shl(12, and(shr(index2, scalar_v), 1)), shl(8, and(shr(index2, scalar_u), 1))))
                        let index3 := sub(index2, 64)
                        let T2 :=
                            add(T3, add(shl(11, and(shr(index3, scalar_v), 1)), shl(7, and(shr(index3, scalar_u), 1))))
                        index := sub(index3, 64)
                        let T1 :=
                            add(T2, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                        //tbd: check validity of formulae with (0,1) to remove conditional jump
                        if iszero(T1) {
                            Y := sub(p, Y)
                            continue
                        }
                        extcodecopy(dataPointer, T, T1, 64)
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        // inlined EcZZ_AddN
                        if iszero(zz) {
                            X := mload(T)
                            Y := mload(add(T, 32))
                            zz := 1
                            zzz := 1
                            continue
                        }
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        let T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        //special case ecAdd(P,P)=EcDbl
                        if iszero(y2) {
                            if iszero(T2) {
                                let T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                let T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                let T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        let T4 := mulmod(T2, T2, p)
                        let T1 := mulmod(T4, T2, p) //
                        zz := mulmod(zz, T4, p)
                        //zzz3=V*ZZ1
                        zzz := mulmod(zzz, T1, p) // W=UV/
                        let zz1 := mulmod(X, T4, p)
                        X := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, X), p), y2, p), mulmod(Y, T1, p), p)
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
   
    // improving the extcodecopy trick : append array at end of contract
    function ecZZ_mulmuladd_S8_hackmem(uint256 scalar_u, uint256 scalar_v, uint256 dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        uint256 zz; // third and  coordinates of the point
        uint256[6] memory T;
        zz = 256; //start index
        unchecked {
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                codecopy(T, add(mload(T), dataPointer), 64)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for { let index := 254 } gt(index, 191) { index := add(index, 191) } {
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    /* compute element to access in precomputed table */
                    T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(12, and(shr(index, scalar_v), 1)), shl(8, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(11, and(shr(index, scalar_v), 1)), shl(7, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                    //index:=add(index,192), restore index, interleaved with loop
                    //tbd: check validity of formulae with (0,1) to remove conditional jump
                    if iszero(T4) {
                        Y := sub(p, Y)
                        continue
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        codecopy(T, add(T4, dataPointer), 64)
                        // inlined EcZZ_AddN
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        T4 := mulmod(T2, T2, p)
                        T1 := mulmod(T4, T2, p)
                        T2 := mulmod(zz, T4, p) // W=UV
                        zzz := mulmod(zzz, T1, p) //zz3=V*ZZ1
                        let zz1 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, T4), p), y2, p), mulmod(Y, T1, p), p)
                        zz := T2
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q stored in contract at address Shamir8
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q appended at end of contract at address endcontract
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    function ecdsa_precomputed_hackmem(bytes32 message, uint256[2] calldata rs, uint256 endcontract)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via bytecode assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = ecZZ_mulmuladd_S8_hackmem(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), endcontract);
        assembly {
            X := addmod(X, sub(n, r), n)
        }
        return X == 0;
    } //end  ecdsa_precomputed_verify()
} //EOF
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.2) (utils/Base64.sol)
pragma solidity ^0.8.20;
/**
 * @dev Provides a set of functions to operate with Base64 strings.
 */
library Base64 {
    /**
     * @dev Base64 Encoding/Decoding Table
     * See sections 4 and 5 of https://datatracker.ietf.org/doc/html/rfc4648
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    string internal constant _TABLE_URL = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_";
    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE, true);
    }
    /**
     * @dev Converts a `bytes` to its Bytes64Url `string` representation.
     */
    function encodeURL(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE_URL, false);
    }
    /**
     * @dev Internal table-agnostic conversion
     */
    function _encode(bytes memory data, string memory table, bool withPadding) private pure returns (string memory) {
        /**
         * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
         * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
         */
        if (data.length == 0) return "";
        // If padding is enabled, the final length should be `bytes` data length divided by 3 rounded up and then
        // multiplied by 4 so that it leaves room for padding the last chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        // - `4 *`              -> 4 characters for each chunk
        // If padding is disabled, the final length should be `bytes` data length multiplied by 4/3 rounded up as
        // opposed to when padding is required to fill the last chunk.
        // - `4 *`              -> 4 characters for each chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        uint256 resultLength = withPadding ? 4 * ((data.length + 2) / 3) : (4 * data.length + 2) / 3;
        string memory result = new string(resultLength);
        /// @solidity memory-safe-assembly
        assembly {
            // Prepare the lookup table (skip the first "length" byte)
            let tablePtr := add(table, 1)
            // Prepare result pointer, jump over length
            let resultPtr := add(result, 0x20)
            let dataPtr := data
            let endPtr := add(data, mload(data))
            // In some cases, the last iteration will read bytes after the end of the data. We cache the value, and
            // set it to zero to make sure no dirty bytes are read in that section.
            let afterPtr := add(endPtr, 0x20)
            let afterCache := mload(afterPtr)
            mstore(afterPtr, 0x00)
            // Run over the input, 3 bytes at a time
            for {
            } lt(dataPtr, endPtr) {
            } {
                // Advance 3 bytes
                dataPtr := add(dataPtr, 3)
                let input := mload(dataPtr)
                // To write each character, shift the 3 byte (24 bits) chunk
                // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
                // and apply logical AND with 0x3F to bitmask the least significant 6 bits.
                // Use this as an index into the lookup table, mload an entire word
                // so the desired character is in the least significant byte, and
                // mstore8 this least significant byte into the result and continue.
                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
            }
            // Reset the value that was cached
            mstore(afterPtr, afterCache)
            if withPadding {
                // When data `bytes` is not exactly 3 bytes long
                // it is padded with `=` characters at the end
                switch mod(mload(data), 3)
                case 1 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                    mstore8(sub(resultPtr, 2), 0x3d)
                }
                case 2 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                }
            }
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Library for converting numbers into strings and other string operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibString.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibString.sol)
///
/// @dev Note:
/// For performance and bytecode compactness, most of the string operations are restricted to
/// byte strings (7-bit ASCII), except where otherwise specified.
/// Usage of byte string operations on charsets with runes spanning two or more bytes
/// can lead to undefined behavior.
library LibString {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                        CUSTOM ERRORS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The length of the output is too small to contain all the hex digits.
    error HexLengthInsufficient();
    /// @dev The length of the string is more than 32 bytes.
    error TooBigForSmallString();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The constant returned when the `search` is not found in the string.
    uint256 internal constant NOT_FOUND = type(uint256).max;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     DECIMAL OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // The maximum value of a uint256 contains 78 digits (1 byte per digit), but
            // we allocate 0xa0 bytes to keep the free memory pointer 32-byte word aligned.
            // We will need 1 word for the trailing zeros padding, 1 word for the length,
            // and 3 words for a maximum of 78 digits.
            str := add(mload(0x40), 0x80)
            // Update the free memory pointer to allocate.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end of the memory to calculate the length later.
            let end := str
            let w := not(0) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 1)`.
                // Write the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(str, add(48, mod(temp, 10)))
                // Keep dividing `temp` until zero.
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let length := sub(end, str)
            // Move the pointer 32 bytes leftwards to make room for the length.
            str := sub(str, 0x20)
            // Store the length.
            mstore(str, length)
        }
    }
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(int256 value) internal pure returns (string memory str) {
        if (value >= 0) {
            return toString(uint256(value));
        }
        unchecked {
            str = toString(~uint256(value) + 1);
        }
        /// @solidity memory-safe-assembly
        assembly {
            // We still have some spare memory space on the left,
            // as we have allocated 3 words (96 bytes) for up to 78 digits.
            let length := mload(str) // Load the string length.
            mstore(str, 0x2d) // Store the '-' character.
            str := sub(str, 1) // Move back the string pointer by a byte.
            mstore(str, add(length, 1)) // Update the string length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   HEXADECIMAL OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2 + 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value, length);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexStringNoPrefix(uint256 value, uint256 length)
        internal
        pure
        returns (string memory str)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, `length * 2` bytes
            // for the digits, 0x02 bytes for the prefix, and 0x20 bytes for the length.
            // We add 0x20 to the total and round down to a multiple of 0x20.
            // (0x20 + 0x20 + 0x02 + 0x20) = 0x62.
            str := add(mload(0x40), and(add(shl(1, length), 0x42), not(0x1f)))
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let start := sub(str, add(length, length))
            let w := not(1) // Tsk.
            let temp := value
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for {} 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(xor(str, start)) { break }
            }
            if temp {
                mstore(0x00, 0x2194895a) // `HexLengthInsufficient()`.
                revert(0x1c, 0x04)
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2 + 2` bytes.
    function toHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x".
    /// The output excludes leading "0" from the `toHexString` output.
    /// `0x00: "0x0", 0x01: "0x1", 0x12: "0x12", 0x123: "0x123"`.
    function toMinimalHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(add(str, o), 0x3078) // Write the "0x" prefix, accounting for leading zero.
            str := sub(add(str, o), 2) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output excludes leading "0" from the `toHexStringNoPrefix` output.
    /// `0x00: "0", 0x01: "1", 0x12: "12", 0x123: "123"`.
    function toMinimalHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := mload(str) // Get the length.
            str := add(str, o) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2` bytes.
    function toHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x40 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x40) is 0xa0.
            str := add(mload(0x40), 0x80)
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let w := not(1) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(temp) { break }
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x", encoded using 2 hexadecimal digits per byte,
    /// and the alphabets are capitalized conditionally according to
    /// https://eips.ethereum.org/EIPS/eip-55
    function toHexStringChecksummed(address value) internal pure returns (string memory str) {
        str = toHexString(value);
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(6, div(not(0), 255)) // `0b010000000100000000 ...`
            let o := add(str, 0x22)
            let hashed := and(keccak256(o, 40), mul(34, mask)) // `0b10001000 ... `
            let t := shl(240, 136) // `0b10001000 << 240`
            for { let i := 0 } 1 {} {
                mstore(add(i, i), mul(t, byte(i, hashed)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
            mstore(o, xor(mload(o), shr(1, and(mload(0x00), and(mload(o), mask)))))
            o := add(o, 0x20)
            mstore(o, xor(mload(o), shr(1, and(mload(0x20), and(mload(o), mask)))))
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    function toHexString(address value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(address value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            str := mload(0x40)
            // Allocate the memory.
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x28 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x28) is 0x80.
            mstore(0x40, add(str, 0x80))
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            str := add(str, 2)
            mstore(str, 40)
            let o := add(str, 0x20)
            mstore(add(o, 40), 0)
            value := shl(96, value)
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let i := 0 } 1 {} {
                let p := add(o, add(i, i))
                let temp := byte(i, value)
                mstore8(add(p, 1), mload(and(temp, 15)))
                mstore8(p, mload(shr(4, temp)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexString(bytes memory raw) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(raw);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(bytes memory raw) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(raw)
            str := add(mload(0x40), 2) // Skip 2 bytes for the optional prefix.
            mstore(str, add(length, length)) // Store the length of the output.
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let o := add(str, 0x20)
            let end := add(raw, length)
            for {} iszero(eq(raw, end)) {} {
                raw := add(raw, 1)
                mstore8(add(o, 1), mload(and(mload(raw), 15)))
                mstore8(o, mload(and(shr(4, mload(raw)), 15)))
                o := add(o, 2)
            }
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(0x40, add(o, 0x20)) // Allocate the memory.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RUNE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the number of UTF characters in the string.
    function runeCount(string memory s) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            if mload(s) {
                mstore(0x00, div(not(0), 255))
                mstore(0x20, 0x0202020202020202020202020202020202020202020202020303030304040506)
                let o := add(s, 0x20)
                let end := add(o, mload(s))
                for { result := 1 } 1 { result := add(result, 1) } {
                    o := add(o, byte(0, mload(shr(250, mload(o)))))
                    if iszero(lt(o, end)) { break }
                }
            }
        }
    }
    /// @dev Returns if this string is a 7-bit ASCII string.
    /// (i.e. all characters codes are in [0..127])
    function is7BitASCII(string memory s) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(7, div(not(0), 255))
            result := 1
            let n := mload(s)
            if n {
                let o := add(s, 0x20)
                let end := add(o, n)
                let last := mload(end)
                mstore(end, 0)
                for {} 1 {} {
                    if and(mask, mload(o)) {
                        result := 0
                        break
                    }
                    o := add(o, 0x20)
                    if iszero(lt(o, end)) { break }
                }
                mstore(end, last)
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   BYTE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    // For performance and bytecode compactness, byte string operations are restricted
    // to 7-bit ASCII strings. All offsets are byte offsets, not UTF character offsets.
    // Usage of byte string operations on charsets with runes spanning two or more bytes
    // can lead to undefined behavior.
    /// @dev Returns `subject` all occurrences of `search` replaced with `replacement`.
    function replace(string memory subject, string memory search, string memory replacement)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            let replacementLength := mload(replacement)
            subject := add(subject, 0x20)
            search := add(search, 0x20)
            replacement := add(replacement, 0x20)
            result := add(mload(0x40), 0x20)
            let subjectEnd := add(subject, subjectLength)
            if iszero(gt(searchLength, subjectLength)) {
                let subjectSearchEnd := add(sub(subjectEnd, searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                mstore(result, t)
                                result := add(result, 1)
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Copy the `replacement` one word at a time.
                        for { let o := 0 } 1 {} {
                            mstore(add(result, o), mload(add(replacement, o)))
                            o := add(o, 0x20)
                            if iszero(lt(o, replacementLength)) { break }
                        }
                        result := add(result, replacementLength)
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    mstore(result, t)
                    result := add(result, 1)
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
            }
            let resultRemainder := result
            result := add(mload(0x40), 0x20)
            let k := add(sub(resultRemainder, result), sub(subjectEnd, subject))
            // Copy the rest of the string one word at a time.
            for {} lt(subject, subjectEnd) {} {
                mstore(resultRemainder, mload(subject))
                resultRemainder := add(resultRemainder, 0x20)
                subject := add(subject, 0x20)
            }
            result := sub(result, 0x20)
            let last := add(add(result, 0x20), k) // Zeroize the slot after the string.
            mstore(last, 0)
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
            mstore(result, k) // Store the length.
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for { let subjectLength := mload(subject) } 1 {} {
                if iszero(mload(search)) {
                    if iszero(gt(from, subjectLength)) {
                        result := from
                        break
                    }
                    result := subjectLength
                    break
                }
                let searchLength := mload(search)
                let subjectStart := add(subject, 0x20)
                result := not(0) // Initialize to `NOT_FOUND`.
                subject := add(subjectStart, from)
                let end := add(sub(add(subjectStart, subjectLength), searchLength), 1)
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(add(search, 0x20))
                if iszero(and(lt(subject, end), lt(from, subjectLength))) { break }
                if iszero(lt(searchLength, 0x20)) {
                    for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                        if iszero(shr(m, xor(mload(subject), s))) {
                            if eq(keccak256(subject, searchLength), h) {
                                result := sub(subject, subjectStart)
                                break
                            }
                        }
                        subject := add(subject, 1)
                        if iszero(lt(subject, end)) { break }
                    }
                    break
                }
                for {} 1 {} {
                    if iszero(shr(m, xor(mload(subject), s))) {
                        result := sub(subject, subjectStart)
                        break
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = indexOf(subject, search, 0);
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                result := not(0) // Initialize to `NOT_FOUND`.
                let searchLength := mload(search)
                if gt(searchLength, mload(subject)) { break }
                let w := result
                let fromMax := sub(mload(subject), searchLength)
                if iszero(gt(fromMax, from)) { from := fromMax }
                let end := add(add(subject, 0x20), w)
                subject := add(add(subject, 0x20), from)
                if iszero(gt(subject, end)) { break }
                // As this function is not too often used,
                // we shall simply use keccak256 for smaller bytecode size.
                for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                    if eq(keccak256(subject, searchLength), h) {
                        result := sub(subject, add(end, 1))
                        break
                    }
                    subject := add(subject, w) // `sub(subject, 1)`.
                    if iszero(gt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = lastIndexOf(subject, search, uint256(int256(-1)));
    }
    /// @dev Returns true if `search` is found in `subject`, false otherwise.
    function contains(string memory subject, string memory search) internal pure returns (bool) {
        return indexOf(subject, search) != NOT_FOUND;
    }
    /// @dev Returns whether `subject` starts with `search`.
    function startsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                iszero(gt(searchLength, mload(subject))),
                eq(
                    keccak256(add(subject, 0x20), searchLength),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns whether `subject` ends with `search`.
    function endsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            let subjectLength := mload(subject)
            // Whether `search` is not longer than `subject`.
            let withinRange := iszero(gt(searchLength, subjectLength))
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                withinRange,
                eq(
                    keccak256(
                        // `subject + 0x20 + max(subjectLength - searchLength, 0)`.
                        add(add(subject, 0x20), mul(withinRange, sub(subjectLength, searchLength))),
                        searchLength
                    ),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns `subject` repeated `times`.
    function repeat(string memory subject, uint256 times)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(or(iszero(times), iszero(subjectLength))) {
                subject := add(subject, 0x20)
                result := mload(0x40)
                let output := add(result, 0x20)
                for {} 1 {} {
                    // Copy the `subject` one word at a time.
                    for { let o := 0 } 1 {} {
                        mstore(add(output, o), mload(add(subject, o)))
                        o := add(o, 0x20)
                        if iszero(lt(o, subjectLength)) { break }
                    }
                    output := add(output, subjectLength)
                    times := sub(times, 1)
                    if iszero(times) { break }
                }
                mstore(output, 0) // Zeroize the slot after the string.
                let resultLength := sub(output, add(result, 0x20))
                mstore(result, resultLength) // Store the length.
                // Allocate the memory.
                mstore(0x40, add(result, add(resultLength, 0x20)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to `end` (exclusive).
    /// `start` and `end` are byte offsets.
    function slice(string memory subject, uint256 start, uint256 end)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(gt(subjectLength, end)) { end := subjectLength }
            if iszero(gt(subjectLength, start)) { start := subjectLength }
            if lt(start, end) {
                result := mload(0x40)
                let resultLength := sub(end, start)
                mstore(result, resultLength)
                subject := add(subject, start)
                let w := not(0x1f)
                // Copy the `subject` one word at a time, backwards.
                for { let o := and(add(resultLength, 0x1f), w) } 1 {} {
                    mstore(add(result, o), mload(add(subject, o)))
                    o := add(o, w) // `sub(o, 0x20)`.
                    if iszero(o) { break }
                }
                // Zeroize the slot after the string.
                mstore(add(add(result, 0x20), resultLength), 0)
                // Allocate memory for the length and the bytes,
                // rounded up to a multiple of 32.
                mstore(0x40, add(result, and(add(resultLength, 0x3f), w)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to the end of the string.
    /// `start` is a byte offset.
    function slice(string memory subject, uint256 start)
        internal
        pure
        returns (string memory result)
    {
        result = slice(subject, start, uint256(int256(-1)));
    }
    /// @dev Returns all the indices of `search` in `subject`.
    /// The indices are byte offsets.
    function indicesOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256[] memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            if iszero(gt(searchLength, subjectLength)) {
                subject := add(subject, 0x20)
                search := add(search, 0x20)
                result := add(mload(0x40), 0x20)
                let subjectStart := subject
                let subjectSearchEnd := add(sub(add(subject, subjectLength), searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Append to `result`.
                        mstore(result, sub(subject, subjectStart))
                        result := add(result, 0x20)
                        // Advance `subject` by `searchLength`.
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
                let resultEnd := result
                // Assign `result` to the free memory pointer.
                result := mload(0x40)
                // Store the length of `result`.
                mstore(result, shr(5, sub(resultEnd, add(result, 0x20))))
                // Allocate memory for result.
                // We allocate one more word, so this array can be recycled for {split}.
                mstore(0x40, add(resultEnd, 0x20))
            }
        }
    }
    /// @dev Returns a arrays of strings based on the `delimiter` inside of the `subject` string.
    function split(string memory subject, string memory delimiter)
        internal
        pure
        returns (string[] memory result)
    {
        uint256[] memory indices = indicesOf(subject, delimiter);
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            let indexPtr := add(indices, 0x20)
            let indicesEnd := add(indexPtr, shl(5, add(mload(indices), 1)))
            mstore(add(indicesEnd, w), mload(subject))
            mstore(indices, add(mload(indices), 1))
            let prevIndex := 0
            for {} 1 {} {
                let index := mload(indexPtr)
                mstore(indexPtr, 0x60)
                if iszero(eq(index, prevIndex)) {
                    let element := mload(0x40)
                    let elementLength := sub(index, prevIndex)
                    mstore(element, elementLength)
                    // Copy the `subject` one word at a time, backwards.
                    for { let o := and(add(elementLength, 0x1f), w) } 1 {} {
                        mstore(add(element, o), mload(add(add(subject, prevIndex), o)))
                        o := add(o, w) // `sub(o, 0x20)`.
                        if iszero(o) { break }
                    }
                    // Zeroize the slot after the string.
                    mstore(add(add(element, 0x20), elementLength), 0)
                    // Allocate memory for the length and the bytes,
                    // rounded up to a multiple of 32.
                    mstore(0x40, add(element, and(add(elementLength, 0x3f), w)))
                    // Store the `element` into the array.
                    mstore(indexPtr, element)
                }
                prevIndex := add(index, mload(delimiter))
                indexPtr := add(indexPtr, 0x20)
                if iszero(lt(indexPtr, indicesEnd)) { break }
            }
            result := indices
            if iszero(mload(delimiter)) {
                result := add(indices, 0x20)
                mstore(result, sub(mload(indices), 2))
            }
        }
    }
    /// @dev Returns a concatenated string of `a` and `b`.
    /// Cheaper than `string.concat()` and does not de-align the free memory pointer.
    function concat(string memory a, string memory b)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            result := mload(0x40)
            let aLength := mload(a)
            // Copy `a` one word at a time, backwards.
            for { let o := and(add(aLength, 0x20), w) } 1 {} {
                mstore(add(result, o), mload(add(a, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let bLength := mload(b)
            let output := add(result, aLength)
            // Copy `b` one word at a time, backwards.
            for { let o := and(add(bLength, 0x20), w) } 1 {} {
                mstore(add(output, o), mload(add(b, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let totalLength := add(aLength, bLength)
            let last := add(add(result, 0x20), totalLength)
            // Zeroize the slot after the string.
            mstore(last, 0)
            // Stores the length.
            mstore(result, totalLength)
            // Allocate memory for the length and the bytes,
            // rounded up to a multiple of 32.
            mstore(0x40, and(add(last, 0x1f), w))
        }
    }
    /// @dev Returns a copy of the string in either lowercase or UPPERCASE.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function toCase(string memory subject, bool toUpper)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(subject)
            if length {
                result := add(mload(0x40), 0x20)
                subject := add(subject, 1)
                let flags := shl(add(70, shl(5, toUpper)), 0x3ffffff)
                let w := not(0)
                for { let o := length } 1 {} {
                    o := add(o, w)
                    let b := and(0xff, mload(add(subject, o)))
                    mstore8(add(result, o), xor(b, and(shr(b, flags), 0x20)))
                    if iszero(o) { break }
                }
                result := mload(0x40)
                mstore(result, length) // Store the length.
                let last := add(add(result, 0x20), length)
                mstore(last, 0) // Zeroize the slot after the string.
                mstore(0x40, add(last, 0x20)) // Allocate the memory.
            }
        }
    }
    /// @dev Returns a string from a small bytes32 string.
    /// `s` must be null-terminated, or behavior will be undefined.
    function fromSmallString(bytes32 s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let n := 0
            for {} byte(n, s) { n := add(n, 1) } {} // Scan for '\\0'.
            mstore(result, n)
            let o := add(result, 0x20)
            mstore(o, s)
            mstore(add(o, n), 0)
            mstore(0x40, add(result, 0x40))
        }
    }
    /// @dev Returns the small string, with all bytes after the first null byte zeroized.
    function normalizeSmallString(bytes32 s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for {} byte(result, s) { result := add(result, 1) } {} // Scan for '\\0'.
            mstore(0x00, s)
            mstore(result, 0x00)
            result := mload(0x00)
        }
    }
    /// @dev Returns the string as a normalized null-terminated small string.
    function toSmallString(string memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(s)
            if iszero(lt(result, 33)) {
                mstore(0x00, 0xec92f9a3) // `TooBigForSmallString()`.
                revert(0x1c, 0x04)
            }
            result := shl(shl(3, sub(32, result)), mload(add(s, result)))
        }
    }
    /// @dev Returns a lowercased copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function lower(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, false);
    }
    /// @dev Returns an UPPERCASED copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function upper(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, true);
    }
    /// @dev Escapes the string to be used within HTML tags.
    function escapeHTML(string memory s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            // Store the bytes of the packed offsets and strides into the scratch space.
            // `packed = (stride << 5) | offset`. Max offset is 20. Max stride is 6.
            mstore(0x1f, 0x900094)
            mstore(0x08, 0xc0000000a6ab)
            // Store "&quot;&amp;&#39;&lt;&gt;" into the scratch space.
            mstore(0x00, shl(64, 0x2671756f743b26616d703b262333393b266c743b2667743b))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                // Not in `["\\"","'","&","<",">"]`.
                if iszero(and(shl(c, 1), 0x500000c400000000)) {
                    mstore8(result, c)
                    result := add(result, 1)
                    continue
                }
                let t := shr(248, mload(c))
                mstore(result, mload(and(t, 0x1f)))
                result := add(result, shr(5, t))
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    /// If `addDoubleQuotes` is true, the result will be enclosed in double-quotes.
    function escapeJSON(string memory s, bool addDoubleQuotes)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            // Store "\\\\u0000" in scratch space.
            // Store "0123456789abcdef" in scratch space.
            // Also, store `{0x08:"b", 0x09:"t", 0x0a:"n", 0x0c:"f", 0x0d:"r"}`.
            // into the scratch space.
            mstore(0x15, 0x5c75303030303031323334353637383961626364656662746e006672)
            // Bitmask for detecting `["\\"","\\\\"]`.
            let e := or(shl(0x22, 1), shl(0x5c, 1))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                if iszero(lt(c, 0x20)) {
                    if iszero(and(shl(c, 1), e)) {
                        // Not in `["\\"","\\\\"]`.
                        mstore8(result, c)
                        result := add(result, 1)
                        continue
                    }
                    mstore8(result, 0x5c) // "\\\\".
                    mstore8(add(result, 1), c)
                    result := add(result, 2)
                    continue
                }
                if iszero(and(shl(c, 1), 0x3700)) {
                    // Not in `["\\b","\\t","\
","\\f","\\d"]`.
                    mstore8(0x1d, mload(shr(4, c))) // Hex value.
                    mstore8(0x1e, mload(and(c, 15))) // Hex value.
                    mstore(result, mload(0x19)) // "\\\\u00XX".
                    result := add(result, 6)
                    continue
                }
                mstore8(result, 0x5c) // "\\\\".
                mstore8(add(result, 1), mload(add(c, 8)))
                result := add(result, 2)
            }
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    function escapeJSON(string memory s) internal pure returns (string memory result) {
        result = escapeJSON(s, false);
    }
    /// @dev Returns whether `a` equals `b`.
    function eq(string memory a, string memory b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := eq(keccak256(add(a, 0x20), mload(a)), keccak256(add(b, 0x20), mload(b)))
        }
    }
    /// @dev Returns whether `a` equals `b`, where `b` is a null-terminated small string.
    function eqs(string memory a, bytes32 b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            // These should be evaluated on compile time, as far as possible.
            let m := not(shl(7, div(not(iszero(b)), 255))) // `0x7f7f ...`.
            let x := not(or(m, or(b, add(m, and(b, m)))))
            let r := shl(7, iszero(iszero(shr(128, x))))
            r := or(r, shl(6, iszero(iszero(shr(64, shr(r, x))))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            result := gt(eq(mload(a), add(iszero(x), xor(31, shr(3, r)))),
                xor(shr(add(8, r), b), shr(add(8, r), mload(add(a, 0x20)))))
        }
    }
    /// @dev Packs a single string with its length into a single word.
    /// Returns `bytes32(0)` if the length is zero or greater than 31.
    function packOne(string memory a) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // We don't need to zero right pad the string,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes.
                    mload(add(a, 0x1f)),
                    // `length != 0 && length < 32`. Abuses underflow.
                    // Assumes that the length is valid and within the block gas limit.
                    lt(sub(mload(a), 1), 0x1f)
                )
        }
    }
    /// @dev Unpacks a string packed using {packOne}.
    /// Returns the empty string if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packOne}, the output behavior is undefined.
    function unpackOne(bytes32 packed) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            result := mload(0x40)
            // Allocate 2 words (1 for the length, 1 for the bytes).
            mstore(0x40, add(result, 0x40))
            // Zeroize the length slot.
            mstore(result, 0)
            // Store the length and bytes.
            mstore(add(result, 0x1f), packed)
            // Right pad with zeroes.
            mstore(add(add(result, 0x20), mload(result)), 0)
        }
    }
    /// @dev Packs two strings with their lengths into a single word.
    /// Returns `bytes32(0)` if combined length is zero or greater than 30.
    function packTwo(string memory a, string memory b) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let aLength := mload(a)
            // We don't need to zero right pad the strings,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes of `a` and `b`.
                    or(
                        shl(shl(3, sub(0x1f, aLength)), mload(add(a, aLength))),
                        mload(sub(add(b, 0x1e), aLength))
                    ),
                    // `totalLength != 0 && totalLength < 31`. Abuses underflow.
                    // Assumes that the lengths are valid and within the block gas limit.
                    lt(sub(add(aLength, mload(b)), 1), 0x1e)
                )
        }
    }
    /// @dev Unpacks strings packed using {packTwo}.
    /// Returns the empty strings if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packTwo}, the output behavior is undefined.
    function unpackTwo(bytes32 packed)
        internal
        pure
        returns (string memory resultA, string memory resultB)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            resultA := mload(0x40)
            resultB := add(resultA, 0x40)
            // Allocate 2 words for each string (1 for the length, 1 for the byte). Total 4 words.
            mstore(0x40, add(resultB, 0x40))
            // Zeroize the length slots.
            mstore(resultA, 0)
            mstore(resultB, 0)
            // Store the lengths and bytes.
            mstore(add(resultA, 0x1f), packed)
            mstore(add(resultB, 0x1f), mload(add(add(resultA, 0x20), mload(resultA))))
            // Right pad with zeroes.
            mstore(add(add(resultA, 0x20), mload(resultA)), 0)
            mstore(add(add(resultB, 0x20), mload(resultB)), 0)
        }
    }
    /// @dev Directly returns `a` without copying.
    function directReturn(string memory a) internal pure {
        assembly {
            // Assumes that the string does not start from the scratch space.
            let retStart := sub(a, 0x20)
            let retSize := add(mload(a), 0x40)
            // Right pad with zeroes. Just in case the string is produced
            // by a method that doesn't zero right pad.
            mstore(add(retStart, retSize), 0)
            // Store the return offset.
            mstore(retStart, 0x20)
            // End the transaction, returning the string.
            return(retStart, retSize)
        }
    }
}