// SPDX-License-Identifier: MIT
pragma solidity 0.8.28;

import "account-abstraction/core/Helpers.sol";

import { IAccount } from "account-abstraction/interfaces/IAccount.sol";
import { IEntryPoint } from "account-abstraction/interfaces/IEntryPoint.sol";
import { UserOperation } from "account-abstraction/interfaces/UserOperation.sol";

import { WebAuthn } from "webauthn-sol/WebAuthn.sol";
import { Receiver } from "solady/accounts/Receiver.sol";

import { IERC1271 } from "@openzeppelin/contracts/interfaces/IERC1271.sol";
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { UUPSUpgradeable } from "@openzeppelin/contracts/proxy/utils/UUPSUpgradeable.sol";

import { ISmartWallet } from "@src/interfaces/internal/ISmartWallet.sol";

/// @title 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.
contract SmartWallet is IERC1271, IAccount, ISmartWallet, Initializable, UUPSUpgradeable, Receiver {
    ISmartWallet.PublicKey public publicKey;

    uint256 private constant _SIG_VALIDATION_FAILED = 1;

    constructor() {
        _disableInitializers();
    }

    /**
     * @dev Initializes the account with a public key
     * @param aPublicKey The public key components [X, Y]
     */
    function initialize(bytes32[2] memory aPublicKey) public virtual initializer {
        publicKey = ISmartWallet.PublicKey(aPublicKey[0], aPublicKey[1]);
        emit AccountInitialized(IEntryPoint(entryPoint()), [publicKey.X, publicKey.Y]);
    }

    /// @notice Reverts if the caller is not the EntryPoint.
    modifier onlyEntryPoint() virtual {
        if (msg.sender != entryPoint()) {
            revert Unauthorized();
        }

        _;
    }

    modifier onlySelf() {
        require(msg.sender == address(this), "only self");
        _;
    }

    /// @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;
    }

    /**
     * @dev ERC1271 signature validation
     * @param message The hash of the data to be signed
     * @param signature The signature byte array associated with _data
     * @return magicValue The bytes4 magic value 0x1626ba7e if valid
     */
    function isValidSignature(
        bytes32 message,
        bytes calldata signature
    )
        external
        view
        override
        returns (bytes4 magicValue)
    {
        if (_validateSignature(abi.encodePacked(message), signature)) {
            return IERC1271(this).isValidSignature.selector;
        }
        return 0xffffffff;
    }

    /// @notice Returns the implementation of the ERC1967 proxy.
    ///
    /// @return $ The address of implementation contract.
    function implementation() public view returns (address $) {
        assembly {
            $ := sload(0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc)
        }
    }

    /// @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))
            }
        }
    }

    /// @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)
    {
        validationData = _validateUserOpSignature(userOp, userOpHash);
    }

    /// @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 onlyEntryPoint {
        _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(ISmartWallet.Call[] calldata calls) external payable virtual onlyEntryPoint {
        for (uint256 i; i < calls.length; i++) {
            _call(calls[i].target, calls[i].value, calls[i].data);
        }
    }

    /// @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))
            }
        }
    }

    /**
     * @dev Validates a WebAuthn signature
     * @param message The message that was signed
     * @param signature The signature data
     * @return bool True if the signature is valid
     */
    function _validateSignature(bytes memory message, bytes calldata signature) private view returns (bool) {
        WebAuthn.WebAuthnAuth memory auth = abi.decode(signature, (WebAuthn.WebAuthnAuth));

        return WebAuthn.verify({
            challenge: message,
            requireUV: false,
            webAuthnAuth: auth,
            x: uint256(publicKey.X),
            y: uint256(publicKey.Y)
        });
    }

    /**
     * @dev Validates the signature of a user operation
     * @param userOp The user operation
     * @param userOpHash The hash of the user operation
     * @return validationData Packed validation data
     */
    function _validateUserOpSignature(
        UserOperation calldata userOp,
        bytes32 userOpHash
    )
        private
        view
        returns (uint256 validationData)
    {
        bytes memory messageToVerify;
        bytes calldata signature;
        ValidationData memory returnIfValid;

        uint256 sigLength = userOp.signature.length;
        if (sigLength == 0) return _SIG_VALIDATION_FAILED;

        uint8 version = uint8(userOp.signature[0]);
        if (version == 1) {
            if (sigLength < 7) return _SIG_VALIDATION_FAILED;
            uint48 validUntil = uint48(bytes6(userOp.signature[1:7]));

            signature = userOp.signature[7:];
            messageToVerify = abi.encodePacked(version, validUntil, userOpHash);
            returnIfValid.validUntil = validUntil;
        } else {
            return _SIG_VALIDATION_FAILED;
        }

        if (_validateSignature(messageToVerify, signature)) {
            return _packValidationData(returnIfValid);
        }
        return _SIG_VALIDATION_FAILED;
    }

    /// @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) onlySelf { }
}

// 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 "./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);
}

/**
 ** 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;

/* 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 ^0.8.0;

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;

/// @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 {
        _beforeReceiverFallbackBody();
        if (_useReceiverFallbackBody()) {
            /// @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`.
                }
            }
        }
        _afterReceiverFallbackBody();
        _;
    }

    /// @dev Whether we want to use the body of the `receiverFallback` modifier.
    function _useReceiverFallbackBody() internal view virtual returns (bool) {
        return true;
    }

    /// @dev Called before the body of the `receiverFallback` modifier.
    function _beforeReceiverFallbackBody() internal virtual {}

    /// @dev Called after the body of the `receiverFallback` modifier.
    function _afterReceiverFallbackBody() internal virtual {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/IERC1271.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-1271 standard signature validation method for
 * contracts as defined in https://eips.ethereum.org/EIPS/eip-1271[ERC-1271].
 */
interface IERC1271 {
    /**
     * @dev Should return whether the signature provided is valid for the provided data
     * @param hash      Hash of the data to be signed
     * @param signature Signature byte array associated with _data
     */
    function isValidSignature(bytes32 hash, bytes memory signature) external view returns (bytes4 magicValue);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.20;

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Storage of the initializable contract.
     *
     * It's implemented on a custom ERC-7201 namespace to reduce the risk of storage collisions
     * when using with upgradeable contracts.
     *
     * @custom:storage-location erc7201:openzeppelin.storage.Initializable
     */
    struct InitializableStorage {
        /**
         * @dev Indicates that the contract has been initialized.
         */
        uint64 _initialized;
        /**
         * @dev Indicates that the contract is in the process of being initialized.
         */
        bool _initializing;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.Initializable")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant INITIALIZABLE_STORAGE = 0xf0c57e16840df040f15088dc2f81fe391c3923bec73e23a9662efc9c229c6a00;

    /**
     * @dev The contract is already initialized.
     */
    error InvalidInitialization();

    /**
     * @dev The contract is not initializing.
     */
    error NotInitializing();

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint64 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that in the context of a constructor an `initializer` may be invoked any
     * number of times. This behavior in the constructor can be useful during testing and is not expected to be used in
     * production.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        // Cache values to avoid duplicated sloads
        bool isTopLevelCall = !$._initializing;
        uint64 initialized = $._initialized;

        // Allowed calls:
        // - initialSetup: the contract is not in the initializing state and no previous version was
        //                 initialized
        // - construction: the contract is initialized at version 1 (no reininitialization) and the
        //                 current contract is just being deployed
        bool initialSetup = initialized == 0 && isTopLevelCall;
        bool construction = initialized == 1 && address(this).code.length == 0;

        if (!initialSetup && !construction) {
            revert InvalidInitialization();
        }
        $._initialized = 1;
        if (isTopLevelCall) {
            $._initializing = true;
        }
        _;
        if (isTopLevelCall) {
            $._initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: Setting the version to 2**64 - 1 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint64 version) {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing || $._initialized >= version) {
            revert InvalidInitialization();
        }
        $._initialized = version;
        $._initializing = true;
        _;
        $._initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        _checkInitializing();
        _;
    }

    /**
     * @dev Reverts if the contract is not in an initializing state. See {onlyInitializing}.
     */
    function _checkInitializing() internal view virtual {
        if (!_isInitializing()) {
            revert NotInitializing();
        }
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing) {
            revert InvalidInitialization();
        }
        if ($._initialized != type(uint64).max) {
            $._initialized = type(uint64).max;
            emit Initialized(type(uint64).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint64) {
        return _getInitializableStorage()._initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _getInitializableStorage()._initializing;
    }

    /**
     * @dev Returns a pointer to the storage namespace.
     */
    // solhint-disable-next-line var-name-mixedcase
    function _getInitializableStorage() private pure returns (InitializableStorage storage $) {
        assembly {
            $.slot := INITIALIZABLE_STORAGE
        }
    }
}

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

pragma solidity ^0.8.20;

import {IERC1822Proxiable} from "../../interfaces/draft-IERC1822.sol";
import {ERC1967Utils} from "../ERC1967/ERC1967Utils.sol";

/**
 * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
 * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
 *
 * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
 * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
 * `UUPSUpgradeable` with a custom implementation of upgrades.
 *
 * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
 */
abstract contract UUPSUpgradeable is IERC1822Proxiable {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable
    address private immutable __self = address(this);

    /**
     * @dev The version of the upgrade interface of the contract. If this getter is missing, both `upgradeTo(address)`
     * and `upgradeToAndCall(address,bytes)` are present, and `upgradeTo` must be used if no function should be called,
     * while `upgradeToAndCall` will invoke the `receive` function if the second argument is the empty byte string.
     * If the getter returns `"5.0.0"`, only `upgradeToAndCall(address,bytes)` is present, and the second argument must
     * be the empty byte string if no function should be called, making it impossible to invoke the `receive` function
     * during an upgrade.
     */
    string public constant UPGRADE_INTERFACE_VERSION = "5.0.0";

    /**
     * @dev The call is from an unauthorized context.
     */
    error UUPSUnauthorizedCallContext();

    /**
     * @dev The storage `slot` is unsupported as a UUID.
     */
    error UUPSUnsupportedProxiableUUID(bytes32 slot);

    /**
     * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
     * a proxy contract with an implementation (as defined in ERC-1967) pointing to self. This should only be the case
     * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
     * function through ERC-1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
     * fail.
     */
    modifier onlyProxy() {
        _checkProxy();
        _;
    }

    /**
     * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
     * callable on the implementing contract but not through proxies.
     */
    modifier notDelegated() {
        _checkNotDelegated();
        _;
    }

    /**
     * @dev Implementation of the ERC-1822 {proxiableUUID} function. This returns the storage slot used by the
     * implementation. It is used to validate the implementation's compatibility when performing an upgrade.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
     */
    function proxiableUUID() external view virtual notDelegated returns (bytes32) {
        return ERC1967Utils.IMPLEMENTATION_SLOT;
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
     * encoded in `data`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) public payable virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, data);
    }

    /**
     * @dev Reverts if the execution is not performed via delegatecall or the execution
     * context is not of a proxy with an ERC-1967 compliant implementation pointing to self.
     * See {_onlyProxy}.
     */
    function _checkProxy() internal view virtual {
        if (
            address(this) == __self || // Must be called through delegatecall
            ERC1967Utils.getImplementation() != __self // Must be called through an active proxy
        ) {
            revert UUPSUnauthorizedCallContext();
        }
    }

    /**
     * @dev Reverts if the execution is performed via delegatecall.
     * See {notDelegated}.
     */
    function _checkNotDelegated() internal view virtual {
        if (address(this) != __self) {
            // Must not be called through delegatecall
            revert UUPSUnauthorizedCallContext();
        }
    }

    /**
     * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
     * {upgradeToAndCall}.
     *
     * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
     *
     * ```solidity
     * function _authorizeUpgrade(address) internal onlyOwner {}
     * ```
     */
    function _authorizeUpgrade(address newImplementation) internal virtual;

    /**
     * @dev Performs an implementation upgrade with a security check for UUPS proxies, and additional setup call.
     *
     * As a security check, {proxiableUUID} is invoked in the new implementation, and the return value
     * is expected to be the implementation slot in ERC-1967.
     *
     * Emits an {IERC1967-Upgraded} event.
     */
    function _upgradeToAndCallUUPS(address newImplementation, bytes memory data) private {
        try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
            if (slot != ERC1967Utils.IMPLEMENTATION_SLOT) {
                revert UUPSUnsupportedProxiableUUID(slot);
            }
            ERC1967Utils.upgradeToAndCall(newImplementation, data);
        } catch {
            // The implementation is not UUPS
            revert ERC1967Utils.ERC1967InvalidImplementation(newImplementation);
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.28;

import { IEntryPoint } from "account-abstraction/interfaces/IEntryPoint.sol";

/// @title Smart Wallet Interface
/// @notice Interface for ERC-4337 compatible smart contract wallet
/// @dev Implements core functionality for smart contract wallet operations
interface ISmartWallet {
    /// @notice Structure representing a WebAuthn public key
    /// @dev Used for signature verification with WebAuthn
    struct PublicKey {
        /// @notice X coordinate of the public key
        /// @dev 32 bytes representing the x-coordinate of the public key point
        bytes32 X;
        /// @notice Y coordinate of the public key
        /// @dev 32 bytes representing the y-coordinate of the public key point
        bytes32 Y;
    }

    /// @notice Represents a call to be executed by the smart wallet
    /// @dev Used for both single and batch transaction executions
    struct Call {
        /// @notice The target contract address to call
        /// @dev The address that will receive the call
        address target;
        /// @notice The amount of native tokens to send with the call
        /// @dev Value in wei to be sent along with the transaction
        uint256 value;
        /// @notice The calldata to be sent with the call
        /// @dev The encoded function call data
        bytes data;
    }

    /// @notice Error thrown when an unauthorized address attempts to perform a restricted action
    /// @dev Used for access control throughout the contract
    error Unauthorized();

    /// @notice Emitted when a new smart wallet account is initialized
    /// @dev Triggered during the initialization of the smart wallet
    /// @param entryPoint The ERC-4337 EntryPoint contract address
    /// @param pubKey The WebAuthn public key components [X, Y]
    event AccountInitialized(IEntryPoint indexed entryPoint, bytes32[2] pubKey);
}

// 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;

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);
}

// 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;
}

//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \  | (__| '_| || | '_ \  _/ _ \ | |__| | '_ \
// |_||_| \___/__/_||_|  \___|_|  \_, | .__/\__\___/ |____|_|_.__/
//                                |__/|_|
///* 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 v5.1.0) (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.
     * Output is not padded with `=` as specified in https://www.rfc-editor.org/rfc/rfc4648[rfc4648].
     */
    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`  -> Prepare for division rounding up
        // - `/ 3`              -> Number of 3-bytes chunks (rounded up)
        // - `4 *`              -> 4 characters for each chunk
        // This is equivalent to: 4 * Math.ceil(data.length / 3)
        //
        // 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 * data.length`  -> 4 characters for each chunk
        // - ` + 2`             -> Prepare for division rounding up
        // - `/ 3`              -> Number of 3-bytes chunks (rounded up)
        // This is equivalent to: Math.ceil((4 * data.length) / 3)
        uint256 resultLength = withPadding ? 4 * ((data.length + 2) / 3) : (4 * data.length + 2) / 3;

        string memory result = new string(resultLength);

        assembly ("memory-safe") {
            // 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();

    /// @dev The input string must be a 7-bit ASCII.
    error StringNot7BitASCII();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The constant returned when the `search` is not found in the string.
    uint256 internal constant NOT_FOUND = type(uint256).max;

    /// @dev Lookup for '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'.
    uint128 internal constant ALPHANUMERIC_7_BIT_ASCII = 0x7fffffe07fffffe03ff000000000000;

    /// @dev Lookup for 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'.
    uint128 internal constant LETTERS_7_BIT_ASCII = 0x7fffffe07fffffe0000000000000000;

    /// @dev Lookup for 'abcdefghijklmnopqrstuvwxyz'.
    uint128 internal constant LOWERCASE_7_BIT_ASCII = 0x7fffffe000000000000000000000000;

    /// @dev Lookup for 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'.
    uint128 internal constant UPPERCASE_7_BIT_ASCII = 0x7fffffe0000000000000000;

    /// @dev Lookup for '0123456789'.
    uint128 internal constant DIGITS_7_BIT_ASCII = 0x3ff000000000000;

    /// @dev Lookup for '0123456789abcdefABCDEF'.
    uint128 internal constant HEXDIGITS_7_BIT_ASCII = 0x7e0000007e03ff000000000000;

    /// @dev Lookup for '01234567'.
    uint128 internal constant OCTDIGITS_7_BIT_ASCII = 0xff000000000000;

    /// @dev Lookup for '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&\'()*+,-./:;<=>?@[\\]^_`{|}~ \t\n\r\x0b\x0c'.
    uint128 internal constant PRINTABLE_7_BIT_ASCII = 0x7fffffffffffffffffffffff00003e00;

    /// @dev Lookup for '!"#$%&\'()*+,-./:;<=>?@[\\]^_`{|}~'.
    uint128 internal constant PUNCTUATION_7_BIT_ASCII = 0x78000001f8000001fc00fffe00000000;

    /// @dev Lookup for ' \t\n\r\x0b\x0c'.
    uint128 internal constant WHITESPACE_7_BIT_ASCII = 0x100003e00;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     DECIMAL OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(uint256 value) internal pure returns (string memory result) {
        /// @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.
            result := add(mload(0x40), 0x80)
            mstore(0x40, add(result, 0x20)) // Allocate memory.
            mstore(result, 0) // Zeroize the slot after the string.

            let end := result // Cache the end of the memory to calculate the length later.
            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 {} {
                result := add(result, w) // `sub(result, 1)`.
                // Store the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(result, add(48, mod(temp, 10)))
                temp := div(temp, 10) // Keep dividing `temp` until zero.
                if iszero(temp) { break }
            }
            let n := sub(end, result)
            result := sub(result, 0x20) // Move the pointer 32 bytes back to make room for the length.
            mstore(result, n) // Store the length.
        }
    }

    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(int256 value) internal pure returns (string memory result) {
        if (value >= 0) return toString(uint256(value));
        unchecked {
            result = 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 n := mload(result) // Load the string length.
            mstore(result, 0x2d) // Store the '-' character.
            result := sub(result, 1) // Move back the string pointer by a byte.
            mstore(result, add(n, 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 result)
    {
        result = toHexStringNoPrefix(value, length);
        /// @solidity memory-safe-assembly
        assembly {
            let n := add(mload(result), 2) // Compute the length.
            mstore(result, 0x3078) // Store the "0x" prefix.
            result := sub(result, 2) // Move the pointer.
            mstore(result, n) // Store the length.
        }
    }

    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is not prefixed with "0x" and is 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 result)
    {
        /// @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.
            result := add(mload(0x40), and(add(shl(1, length), 0x42), not(0x1f)))
            mstore(0x40, add(result, 0x20)) // Allocate memory.
            mstore(result, 0) // Zeroize the slot after the string.

            let end := result // Cache the end to calculate the length later.
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)

            let start := sub(result, 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 {} {
                result := add(result, w) // `sub(result, 2)`.
                mstore8(add(result, 1), mload(and(temp, 15)))
                mstore8(result, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(xor(result, start)) { break }
            }
            if temp {
                mstore(0x00, 0x2194895a) // `HexLengthInsufficient()`.
                revert(0x1c, 0x04)
            }
            let n := sub(end, result)
            result := sub(result, 0x20)
            mstore(result, n) // Store the length.
        }
    }

    /// @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 result) {
        result = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let n := add(mload(result), 2) // Compute the length.
            mstore(result, 0x3078) // Store the "0x" prefix.
            result := sub(result, 2) // Move the pointer.
            mstore(result, n) // Store 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 result) {
        result = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(result, 0x20))), 0x30) // Whether leading zero is present.
            let n := add(mload(result), 2) // Compute the length.
            mstore(add(result, o), 0x3078) // Store the "0x" prefix, accounting for leading zero.
            result := sub(add(result, o), 2) // Move the pointer, accounting for leading zero.
            mstore(result, sub(n, o)) // Store 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 result)
    {
        result = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(result, 0x20))), 0x30) // Whether leading zero is present.
            let n := mload(result) // Get the length.
            result := add(result, o) // Move the pointer, accounting for leading zero.
            mstore(result, sub(n, o)) // Store 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 result) {
        /// @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.
            result := add(mload(0x40), 0x80)
            mstore(0x40, add(result, 0x20)) // Allocate memory.
            mstore(result, 0) // Zeroize the slot after the string.

            let end := result // Cache the end to calculate the length later.
            mstore(0x0f, 0x30313233343536373839616263646566) // Store the "0123456789abcdef" lookup.

            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 {} {
                result := add(result, w) // `sub(result, 2)`.
                mstore8(add(result, 1), mload(and(temp, 15)))
                mstore8(result, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(temp) { break }
            }
            let n := sub(end, result)
            result := sub(result, 0x20)
            mstore(result, n) // Store the length.
        }
    }

    /// @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 result) {
        result = toHexString(value);
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(6, div(not(0), 255)) // `0b010000000100000000 ...`
            let o := add(result, 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 result) {
        result = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let n := add(mload(result), 2) // Compute the length.
            mstore(result, 0x3078) // Store the "0x" prefix.
            result := sub(result, 2) // Move the pointer.
            mstore(result, n) // Store 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 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            // Allocate 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(result, 0x80))
            mstore(0x0f, 0x30313233343536373839616263646566) // Store the "0123456789abcdef" lookup.

            result := add(result, 2)
            mstore(result, 40) // Store the length.
            let o := add(result, 0x20)
            mstore(add(o, 40), 0) // Zeroize the slot after the string.
            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 result) {
        result = toHexStringNoPrefix(raw);
        /// @solidity memory-safe-assembly
        assembly {
            let n := add(mload(result), 2) // Compute the length.
            mstore(result, 0x3078) // Store the "0x" prefix.
            result := sub(result, 2) // Move the pointer.
            mstore(result, n) // Store 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 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let n := mload(raw)
            result := add(mload(0x40), 2) // Skip 2 bytes for the optional prefix.
            mstore(result, add(n, n)) // Store the length of the output.

            mstore(0x0f, 0x30313233343536373839616263646566) // Store the "0123456789abcdef" lookup.
            let o := add(result, 0x20)
            let end := add(raw, n)
            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 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 {
            result := 1
            let mask := shl(7, div(not(0), 255))
            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)
            }
        }
    }

    /// @dev Returns if this string is a 7-bit ASCII string,
    /// AND all characters are in the `allowed` lookup.
    /// Note: If `s` is empty, returns true regardless of `allowed`.
    function is7BitASCII(string memory s, uint128 allowed) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := 1
            if mload(s) {
                let allowed_ := shr(128, shl(128, allowed))
                let o := add(s, 0x20)
                for { let end := add(o, mload(s)) } 1 {} {
                    result := and(result, shr(byte(0, mload(o)), allowed_))
                    o := add(o, 1)
                    if iszero(and(result, lt(o, end))) { break }
                }
            }
        }
    }

    /// @dev Converts the bytes in the 7-bit ASCII string `s` to
    /// an allowed lookup for use in `is7BitASCII(s, allowed)`.
    /// To save runtime gas, you can cache the result in an immutable variable.
    function to7BitASCIIAllowedLookup(string memory s) internal pure returns (uint128 result) {
        /// @solidity memory-safe-assembly
        assembly {
            if mload(s) {
                let o := add(s, 0x20)
                for { let end := add(o, mload(s)) } 1 {} {
                    result := or(result, shl(byte(0, mload(o)), 1))
                    o := add(o, 1)
                    if iszero(lt(o, end)) { break }
                }
                if shr(128, result) {
                    mstore(0x00, 0xc9807e0d) // `StringNot7BitASCII()`.
                    revert(0x1c, 0x04)
                }
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   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 `needle` replaced with `replacement`.
    function replace(string memory subject, string memory needle, string memory replacement)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let needleLen := mload(needle)
            let replacementLen := mload(replacement)
            let d := sub(result, subject) // Memory difference.
            let i := add(subject, 0x20) // Subject bytes pointer.
            let end := add(i, mload(subject))
            if iszero(gt(needleLen, mload(subject))) {
                let subjectSearchEnd := add(sub(end, needleLen), 1)
                let h := 0 // The hash of `needle`.
                if iszero(lt(needleLen, 0x20)) { h := keccak256(add(needle, 0x20), needleLen) }
                let s := mload(add(needle, 0x20))
                for { let m := shl(3, sub(0x20, and(needleLen, 0x1f))) } 1 {} {
                    let t := mload(i)
                    // Whether the first `needleLen % 32` bytes of `subject` and `needle` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(i, needleLen), h)) {
                                mstore(add(i, d), t)
                                i := add(i, 1)
                                if iszero(lt(i, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Copy the `replacement` one word at a time.
                        for { let j := 0 } 1 {} {
                            mstore(add(add(i, d), j), mload(add(add(replacement, 0x20), j)))
                            j := add(j, 0x20)
                            if iszero(lt(j, replacementLen)) { break }
                        }
                        d := sub(add(d, replacementLen), needleLen)
                        if needleLen {
                            i := add(i, needleLen)
                            if iszero(lt(i, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    mstore(add(i, d), t)
                    i := add(i, 1)
                    if iszero(lt(i, subjectSearchEnd)) { break }
                }
            }
            let n := add(sub(d, add(result, 0x20)), end)
            // Copy the rest of the string one word at a time.
            for {} lt(i, end) { i := add(i, 0x20) } { mstore(add(i, d), mload(i)) }
            let o := add(i, d)
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(0x40, add(o, 0x20)) // Allocate memory.
            mstore(result, n) // Store the length.
        }
    }

    /// @dev Returns the byte index of the first location of `needle` in `subject`,
    /// needleing from left to right, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `needle` is not found.
    function indexOf(string memory subject, string memory needle, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := not(0) // Initialize to `NOT_FOUND`.
            for { let subjectLen := mload(subject) } 1 {} {
                if iszero(mload(needle)) {
                    result := from
                    if iszero(gt(from, subjectLen)) { break }
                    result := subjectLen
                    break
                }
                let needleLen := mload(needle)
                let subjectStart := add(subject, 0x20)

                subject := add(subjectStart, from)
                let end := add(sub(add(subjectStart, subjectLen), needleLen), 1)
                let m := shl(3, sub(0x20, and(needleLen, 0x1f)))
                let s := mload(add(needle, 0x20))

                if iszero(and(lt(subject, end), lt(from, subjectLen))) { break }

                if iszero(lt(needleLen, 0x20)) {
                    for { let h := keccak256(add(needle, 0x20), needleLen) } 1 {} {
                        if iszero(shr(m, xor(mload(subject), s))) {
                            if eq(keccak256(subject, needleLen), 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 `needle` in `subject`,
    /// needleing from left to right.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `needle` is not found.
    function indexOf(string memory subject, string memory needle)
        internal
        pure
        returns (uint256 result)
    {
        result = indexOf(subject, needle, 0);
    }

    /// @dev Returns the byte index of the first location of `needle` in `subject`,
    /// needleing from right to left, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `needle` is not found.
    function lastIndexOf(string memory subject, string memory needle, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                result := not(0) // Initialize to `NOT_FOUND`.
                let needleLen := mload(needle)
                if gt(needleLen, mload(subject)) { break }
                let w := result

                let fromMax := sub(mload(subject), needleLen)
                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(needle, 0x20), needleLen) } 1 {} {
                    if eq(keccak256(subject, needleLen), 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 `needle` in `subject`,
    /// needleing from right to left.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `needle` is not found.
    function lastIndexOf(string memory subject, string memory needle)
        internal
        pure
        returns (uint256 result)
    {
        result = lastIndexOf(subject, needle, type(uint256).max);
    }

    /// @dev Returns true if `needle` is found in `subject`, false otherwise.
    function contains(string memory subject, string memory needle) internal pure returns (bool) {
        return indexOf(subject, needle) != NOT_FOUND;
    }

    /// @dev Returns whether `subject` starts with `needle`.
    function startsWith(string memory subject, string memory needle)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let needleLen := mload(needle)
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                iszero(gt(needleLen, mload(subject))),
                eq(
                    keccak256(add(subject, 0x20), needleLen),
                    keccak256(add(needle, 0x20), needleLen)
                )
            )
        }
    }

    /// @dev Returns whether `subject` ends with `needle`.
    function endsWith(string memory subject, string memory needle)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let needleLen := mload(needle)
            // Whether `needle` is not longer than `subject`.
            let inRange := iszero(gt(needleLen, mload(subject)))
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                eq(
                    keccak256(
                        // `subject + 0x20 + max(subjectLen - needleLen, 0)`.
                        add(add(subject, 0x20), mul(inRange, sub(mload(subject), needleLen))),
                        needleLen
                    ),
                    keccak256(add(needle, 0x20), needleLen)
                ),
                inRange
            )
        }
    }

    /// @dev Returns `subject` repeated `times`.
    function repeat(string memory subject, uint256 times)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLen := mload(subject)
            if iszero(or(iszero(times), iszero(subjectLen))) {
                result := mload(0x40)
                subject := add(subject, 0x20)
                let o := add(result, 0x20)
                for {} 1 {} {
                    // Copy the `subject` one word at a time.
                    for { let j := 0 } 1 {} {
                        mstore(add(o, j), mload(add(subject, j)))
                        j := add(j, 0x20)
                        if iszero(lt(j, subjectLen)) { break }
                    }
                    o := add(o, subjectLen)
                    times := sub(times, 1)
                    if iszero(times) { break }
                }
                mstore(o, 0) // Zeroize the slot after the string.
                mstore(0x40, add(o, 0x20)) // Allocate memory.
                mstore(result, sub(o, add(result, 0x20))) // Store the length.
            }
        }
    }

    /// @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 subjectLen := mload(subject)
            if iszero(gt(subjectLen, end)) { end := subjectLen }
            if iszero(gt(subjectLen, start)) { start := subjectLen }
            if lt(start, end) {
                result := mload(0x40)
                let n := sub(end, start)
                let i := add(subject, start)
                let w := not(0x1f)
                // Copy the `subject` one word at a time, backwards.
                for { let j := and(add(n, 0x1f), w) } 1 {} {
                    mstore(add(result, j), mload(add(i, j)))
                    j := add(j, w) // `sub(j, 0x20)`.
                    if iszero(j) { break }
                }
                let o := add(add(result, 0x20), n)
                mstore(o, 0) // Zeroize the slot after the string.
                mstore(0x40, add(o, 0x20)) // Allocate memory.
                mstore(result, n) // Store the length.
            }
        }
    }

    /// @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, type(uint256).max);
    }

    /// @dev Returns all the indices of `needle` in `subject`.
    /// The indices are byte offsets.
    function indicesOf(string memory subject, string memory needle)
        internal
        pure
        returns (uint256[] memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLen := mload(needle)
            if iszero(gt(searchLen, mload(subject))) {
                result := mload(0x40)
                let i := add(subject, 0x20)
                let o := add(result, 0x20)
                let subjectSearchEnd := add(sub(add(i, mload(subject)), searchLen), 1)
                let h := 0 // The hash of `needle`.
                if iszero(lt(searchLen, 0x20)) { h := keccak256(add(needle, 0x20), searchLen) }
                let s := mload(add(needle, 0x20))
                for { let m := shl(3, sub(0x20, and(searchLen, 0x1f))) } 1 {} {
                    let t := mload(i)
                    // Whether the first `searchLen % 32` bytes of `subject` and `needle` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(i, searchLen), h)) {
                                i := add(i, 1)
                                if iszero(lt(i, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        mstore(o, sub(i, add(subject, 0x20))) // Append to `result`.
                        o := add(o, 0x20)
                        i := add(i, searchLen) // Advance `i` by `searchLen`.
                        if searchLen {
                            if iszero(lt(i, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    i := add(i, 1)
                    if iszero(lt(i, subjectSearchEnd)) { break }
                }
                mstore(result, shr(5, sub(o, add(result, 0x20)))) // Store the length of `result`.
                // Allocate memory for result.
                // We allocate one more word, so this array can be recycled for {split}.
                mstore(0x40, add(o, 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))
            for { let prevIndex := 0 } 1 {} {
                let index := mload(indexPtr)
                mstore(indexPtr, 0x60)
                if iszero(eq(index, prevIndex)) {
                    let element := mload(0x40)
                    let l := sub(index, prevIndex)
                    mstore(element, l) // Store the length of the element.
                    // Copy the `subject` one word at a time, backwards.
                    for { let o := and(add(l, 0x1f), w) } 1 {} {
                        mstore(add(element, o), mload(add(add(subject, prevIndex), o)))
                        o := add(o, w) // `sub(o, 0x20)`.
                        if iszero(o) { break }
                    }
                    mstore(add(add(element, 0x20), l), 0) // Zeroize the slot after the string.
                    // Allocate memory for the length and the bytes, rounded up to a multiple of 32.
                    mstore(0x40, add(element, and(add(l, 0x3f), w)))
                    mstore(indexPtr, element) // Store the `element` into the array.
                }
                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 {
            result := mload(0x40)
            let w := not(0x1f)
            let aLen := mload(a)
            // Copy `a` one word at a time, backwards.
            for { let o := and(add(aLen, 0x20), w) } 1 {} {
                mstore(add(result, o), mload(add(a, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let bLen := mload(b)
            let output := add(result, aLen)
            // Copy `b` one word at a time, backwards.
            for { let o := and(add(bLen, 0x20), w) } 1 {} {
                mstore(add(output, o), mload(add(b, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let totalLen := add(aLen, bLen)
            let last := add(add(result, 0x20), totalLen)
            mstore(last, 0) // Zeroize the slot after the string.
            mstore(result, totalLen) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate memory.
        }
    }

    /// @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 n := mload(subject)
            if n {
                result := mload(0x40)
                let o := add(result, 0x20)
                let d := sub(subject, result)
                let flags := shl(add(70, shl(5, toUpper)), 0x3ffffff)
                for { let end := add(o, n) } 1 {} {
                    let b := byte(0, mload(add(d, o)))
                    mstore8(o, xor(and(shr(b, flags), 0x20), b))
                    o := add(o, 1)
                    if eq(o, end) { break }
                }
                mstore(result, n) // Store the length.
                mstore(o, 0) // Zeroize the slot after the string.
                mstore(0x40, add(o, 0x20)) // Allocate 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) // Store the length.
            let o := add(result, 0x20)
            mstore(o, s) // Store the bytes of the string.
            mstore(add(o, n), 0) // Zeroize the slot after the string.
            mstore(0x40, add(result, 0x40)) // Allocate memory.
        }
    }

    /// @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 {
            result := mload(0x40)
            let end := add(s, mload(s))
            let o := add(result, 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(o, c)
                    o := add(o, 1)
                    continue
                }
                let t := shr(248, mload(c))
                mstore(o, mload(and(t, 0x1f)))
                o := add(o, shr(5, t))
            }
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(result, sub(o, add(result, 0x20))) // Store the length.
            mstore(0x40, add(o, 0x20)) // Allocate 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 {
            result := mload(0x40)
            let o := add(result, 0x20)
            if addDoubleQuotes {
                mstore8(o, 34)
                o := add(1, o)
            }
            // 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 { let end := add(s, mload(s)) } 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(o, c)
                        o := add(o, 1)
                        continue
                    }
                    mstore8(o, 0x5c) // "\\".
                    mstore8(add(o, 1), c)
                    o := add(o, 2)
                    continue
                }
                if iszero(and(shl(c, 1), 0x3700)) {
                    // Not in `["\b","\t","\n","\f","\d"]`.
                    mstore8(0x1d, mload(shr(4, c))) // Hex value.
                    mstore8(0x1e, mload(and(c, 15))) // Hex value.
                    mstore(o, mload(0x19)) // "\\u00XX".
                    o := add(o, 6)
                    continue
                }
                mstore8(o, 0x5c) // "\\".
                mstore8(add(o, 1), mload(add(c, 8)))
                o := add(o, 2)
            }
            if addDoubleQuotes {
                mstore8(o, 34)
                o := add(1, o)
            }
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(result, sub(o, add(result, 0x20))) // Store the length.
            mstore(0x40, add(o, 0x20)) // Allocate 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 Encodes `s` so that it can be safely used in a URI,
    /// just like `encodeURIComponent` in JavaScript.
    /// See: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/encodeURIComponent
    /// See: https://datatracker.ietf.org/doc/html/rfc2396
    /// See: https://datatracker.ietf.org/doc/html/rfc3986
    function encodeURIComponent(string memory s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            // Store "0123456789ABCDEF" in scratch space.
            // Uppercased to be consistent with JavaScript's implementation.
            mstore(0x0f, 0x30313233343536373839414243444546)
            let o := add(result, 0x20)
            for { let end := add(s, mload(s)) } iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                // If not in `[0-9A-Z-a-z-_.!~*'()]`.
                if iszero(and(1, shr(c, 0x47fffffe87fffffe03ff678200000000))) {
                    mstore8(o, 0x25) // '%'.
                    mstore8(add(o, 1), mload(and(shr(4, c), 15)))
                    mstore8(add(o, 2), mload(and(c, 15)))
                    o := add(o, 3)
                    continue
                }
                mstore8(o, c)
                o := add(o, 1)
            }
            mstore(result, sub(o, add(result, 0x20))) // Store the length.
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(0x40, add(o, 0x20)) // Allocate memory.
        }
    }

    /// @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 {
            result := mload(0x40) // Grab the free memory pointer.
            mstore(0x40, add(result, 0x40)) // Allocate 2 words (1 for the length, 1 for the bytes).
            mstore(result, 0) // Zeroize the length slot.
            mstore(add(result, 0x1f), packed) // Store the length and bytes.
            mstore(add(add(result, 0x20), mload(result)), 0) // Right pad with zeroes.
        }
    }

    /// @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 aLen := mload(a)
            // We don't need to zero right pad the strings,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    or( // Load the length and the bytes of `a` and `b`.
                    shl(shl(3, sub(0x1f, aLen)), mload(add(a, aLen))), mload(sub(add(b, 0x1e), aLen))),
                    // `totalLen != 0 && totalLen < 31`. Abuses underflow.
                    // Assumes that the lengths are valid and within the block gas limit.
                    lt(sub(add(aLen, 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 {
            resultA := mload(0x40) // Grab the free memory pointer.
            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 retUnpaddedSize := 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, retUnpaddedSize), 0)
            mstore(retStart, 0x20) // Store the return offset.
            // End the transaction, returning the string.
            return(retStart, and(not(0x1f), add(0x1f, retUnpaddedSize)))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.20;

/**
 * @dev ERC-1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (proxy/ERC1967/ERC1967Utils.sol)

pragma solidity ^0.8.21;

import {IBeacon} from "../beacon/IBeacon.sol";
import {IERC1967} from "../../interfaces/IERC1967.sol";
import {Address} from "../../utils/Address.sol";
import {StorageSlot} from "../../utils/StorageSlot.sol";

/**
 * @dev This library provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[ERC-1967] slots.
 */
library ERC1967Utils {
    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev The `implementation` of the proxy is invalid.
     */
    error ERC1967InvalidImplementation(address implementation);

    /**
     * @dev The `admin` of the proxy is invalid.
     */
    error ERC1967InvalidAdmin(address admin);

    /**
     * @dev The `beacon` of the proxy is invalid.
     */
    error ERC1967InvalidBeacon(address beacon);

    /**
     * @dev An upgrade function sees `msg.value > 0` that may be lost.
     */
    error ERC1967NonPayable();

    /**
     * @dev Returns the current implementation address.
     */
    function getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the ERC-1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        if (newImplementation.code.length == 0) {
            revert ERC1967InvalidImplementation(newImplementation);
        }
        StorageSlot.getAddressSlot(IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Performs implementation upgrade with additional setup call if data is nonempty.
     * This function is payable only if the setup call is performed, otherwise `msg.value` is rejected
     * to avoid stuck value in the contract.
     *
     * Emits an {IERC1967-Upgraded} event.
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) internal {
        _setImplementation(newImplementation);
        emit IERC1967.Upgraded(newImplementation);

        if (data.length > 0) {
            Address.functionDelegateCall(newImplementation, data);
        } else {
            _checkNonPayable();
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Returns the current admin.
     *
     * TIP: To get this value clients can read directly from the storage slot shown below (specified by ERC-1967) using
     * the https://eth.wiki/json-rpc/API#eth_getstorageat[`eth_getStorageAt`] RPC call.
     * `0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103`
     */
    function getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the ERC-1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        if (newAdmin == address(0)) {
            revert ERC1967InvalidAdmin(address(0));
        }
        StorageSlot.getAddressSlot(ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {IERC1967-AdminChanged} event.
     */
    function changeAdmin(address newAdmin) internal {
        emit IERC1967.AdminChanged(getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is the keccak-256 hash of "eip1967.proxy.beacon" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Returns the current beacon.
     */
    function getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the ERC-1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        if (newBeacon.code.length == 0) {
            revert ERC1967InvalidBeacon(newBeacon);
        }

        StorageSlot.getAddressSlot(BEACON_SLOT).value = newBeacon;

        address beaconImplementation = IBeacon(newBeacon).implementation();
        if (beaconImplementation.code.length == 0) {
            revert ERC1967InvalidImplementation(beaconImplementation);
        }
    }

    /**
     * @dev Change the beacon and trigger a setup call if data is nonempty.
     * This function is payable only if the setup call is performed, otherwise `msg.value` is rejected
     * to avoid stuck value in the contract.
     *
     * Emits an {IERC1967-BeaconUpgraded} event.
     *
     * CAUTION: Invoking this function has no effect on an instance of {BeaconProxy} since v5, since
     * it uses an immutable beacon without looking at the value of the ERC-1967 beacon slot for
     * efficiency.
     */
    function upgradeBeaconToAndCall(address newBeacon, bytes memory data) internal {
        _setBeacon(newBeacon);
        emit IERC1967.BeaconUpgraded(newBeacon);

        if (data.length > 0) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        } else {
            _checkNonPayable();
        }
    }

    /**
     * @dev Reverts if `msg.value` is not zero. It can be used to avoid `msg.value` stuck in the contract
     * if an upgrade doesn't perform an initialization call.
     */
    function _checkNonPayable() private {
        if (msg.value > 0) {
            revert ERC1967NonPayable();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.20;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {UpgradeableBeacon} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC1967.sol)

pragma solidity ^0.8.20;

/**
 * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
 */
interface IERC1967 {
    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Emitted when the beacon is changed.
     */
    event BeaconUpgraded(address indexed beacon);
}

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

pragma solidity ^0.8.20;

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

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev There's no code at `target` (it is not a contract).
     */
    error AddressEmptyCode(address target);

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.20/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        if (address(this).balance < amount) {
            revert Errors.InsufficientBalance(address(this).balance, amount);
        }

        (bool success, ) = recipient.call{value: amount}("");
        if (!success) {
            revert Errors.FailedCall();
        }
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason or custom error, it is bubbled
     * up by this function (like regular Solidity function calls). However, if
     * the call reverted with no returned reason, this function reverts with a
     * {Errors.FailedCall} error.
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and reverts if the target
     * was not a contract or bubbling up the revert reason (falling back to {Errors.FailedCall}) in case
     * of an unsuccessful call.
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata
    ) internal view returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            // only check if target is a contract if the call was successful and the return data is empty
            // otherwise we already know that it was a contract
            if (returndata.length == 0 && target.code.length == 0) {
                revert AddressEmptyCode(target);
            }
            return returndata;
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and reverts if it wasn't, either by bubbling the
     * revert reason or with a default {Errors.FailedCall} error.
     */
    function verifyCallResult(bool success, bytes memory returndata) internal pure returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            return returndata;
        }
    }

    /**
     * @dev Reverts with returndata if present. Otherwise reverts with {Errors.FailedCall}.
     */
    function _revert(bytes memory returndata) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            assembly ("memory-safe") {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert Errors.FailedCall();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns a `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }
}

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

pragma solidity ^0.8.20;

/**
 * @dev Collection of common custom errors used in multiple contracts
 *
 * IMPORTANT: Backwards compatibility is not guaranteed in future versions of the library.
 * It is recommended to avoid relying on the error API for critical functionality.
 *
 * _Available since v5.1._
 */
library Errors {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error InsufficientBalance(uint256 balance, uint256 needed);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedCall();

    /**
     * @dev The deployment failed.
     */
    error FailedDeployment();

    /**
     * @dev A necessary precompile is missing.
     */
    error MissingPrecompile(address);
}

{
  "remappings": [
    "@openzeppelin/contracts-upgradeable/=lib/openzeppelin-contracts-upgradeable/contracts/",
    "@openzeppelin/contracts/=lib/openzeppelin-contracts-upgradeable/lib/openzeppelin-contracts/contracts/",
    "FreshCryptoLib/=lib/webauthn-sol/lib/FreshCryptoLib/solidity/src/",
    "account-abstraction/=lib/account-abstraction/contracts/",
    "ds-test/=lib/openzeppelin-contracts-upgradeable/lib/forge-std/lib/ds-test/src/",
    "erc4626-tests/=lib/openzeppelin-contracts-upgradeable/lib/erc4626-tests/",
    "forge-std/=lib/forge-std/src/",
    "halmos-cheatcodes/=lib/openzeppelin-contracts-upgradeable/lib/halmos-cheatcodes/src/",
    "openzeppelin-contracts-upgradeable/=lib/openzeppelin-contracts-upgradeable/",
    "openzeppelin-contracts/=lib/openzeppelin-contracts-upgradeable/lib/openzeppelin-contracts/",
    "openzeppelin-foundry-upgrades/=lib/openzeppelin-foundry-upgrades/src/",
    "solady/=lib/solady/src/",
    "solidity-stringutils/=lib/openzeppelin-foundry-upgrades/lib/solidity-stringutils/",
    "webauthn-sol/=lib/webauthn-sol/src/",
    "@src/=src/",
    "@test/=test/",
    "@script/=script/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 800
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "none",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "shanghai",
  "viaIR": false,
  "libraries": {}
}

[{"inputs":[],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[{"internalType":"address","name":"target","type":"address"}],"name":"AddressEmptyCode","type":"error"},{"inputs":[{"internalType":"address","name":"implementation","type":"address"}],"name":"ERC1967InvalidImplementation","type":"error"},{"inputs":[],"name":"ERC1967NonPayable","type":"error"},{"inputs":[],"name":"FailedCall","type":"error"},{"inputs":[],"name":"InvalidInitialization","type":"error"},{"inputs":[],"name":"NotInitializing","type":"error"},{"inputs":[],"name":"UUPSUnauthorizedCallContext","type":"error"},{"inputs":[{"internalType":"bytes32","name":"slot","type":"bytes32"}],"name":"UUPSUnsupportedProxiableUUID","type":"error"},{"inputs":[],"name":"Unauthorized","type":"error"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"contract IEntryPoint","name":"entryPoint","type":"address"},{"indexed":false,"internalType":"bytes32[2]","name":"pubKey","type":"bytes32[2]"}],"name":"AccountInitialized","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint64","name":"version","type":"uint64"}],"name":"Initialized","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"implementation","type":"address"}],"name":"Upgraded","type":"event"},{"stateMutability":"payable","type":"fallback"},{"inputs":[],"name":"UPGRADE_INTERFACE_VERSION","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"entryPoint","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"target","type":"address"},{"internalType":"uint256","name":"value","type":"uint256"},{"internalType":"bytes","name":"data","type":"bytes"}],"name":"execute","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"components":[{"internalType":"address","name":"target","type":"address"},{"internalType":"uint256","name":"value","type":"uint256"},{"internalType":"bytes","name":"data","type":"bytes"}],"internalType":"struct ISmartWallet.Call[]","name":"calls","type":"tuple[]"}],"name":"executeBatch","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[],"name":"implementation","outputs":[{"internalType":"address","name":"$","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"bytes32[2]","name":"aPublicKey","type":"bytes32[2]"}],"name":"initialize","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"bytes32","name":"message","type":"bytes32"},{"internalType":"bytes","name":"signature","type":"bytes"}],"name":"isValidSignature","outputs":[{"internalType":"bytes4","name":"magicValue","type":"bytes4"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"proxiableUUID","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"publicKey","outputs":[{"internalType":"bytes32","name":"X","type":"bytes32"},{"internalType":"bytes32","name":"Y","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"newImplementation","type":"address"},{"internalType":"bytes","name":"data","type":"bytes"}],"name":"upgradeToAndCall","outputs":[],"stateMutability":"payable","type":"function"},{"inputs":[{"components":[{"internalType":"address","name":"sender","type":"address"},{"internalType":"uint256","name":"nonce","type":"uint256"},{"internalType":"bytes","name":"initCode","type":"bytes"},{"internalType":"bytes","name":"callData","type":"bytes"},{"internalType":"uint256","name":"callGasLimit","type":"uint256"},{"internalType":"uint256","name":"verificationGasLimit","type":"uint256"},{"internalType":"uint256","name":"preVerificationGas","type":"uint256"},{"internalType":"uint256","name":"maxFeePerGas","type":"uint256"},{"internalType":"uint256","name":"maxPriorityFeePerGas","type":"uint256"},{"internalType":"bytes","name":"paymasterAndData","type":"bytes"},{"internalType":"bytes","name":"signature","type":"bytes"}],"internalType":"struct UserOperation","name":"userOp","type":"tuple"},{"internalType":"bytes32","name":"userOpHash","type":"bytes32"},{"internalType":"uint256","name":"missingAccountFunds","type":"uint256"}],"name":"validateUserOp","outputs":[{"internalType":"uint256","name":"validationData","type":"uint256"}],"stateMutability":"nonpayable","type":"function"},{"stateMutability":"payable","type":"receive"}]