// File: contracts/CookiCards.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

import {Base64} from "openzeppelin/utils/Base64.sol";
import {Strings} from "openzeppelin/utils/Strings.sol";
import {Ownable} from "openzeppelin/access/Ownable.sol";
import {ICookiStructs} from "./interfaces/ICookiStructs.sol";

contract CookiCards is Ownable, ICookiStructs {
    uint256 public totalSupply;
    uint256 public fee;

    string[] public backgroundColours;
    DoubleString[] public faceColours;
    TripleString[] public hatColours;
    DoubleString[] public neutralColours;

    event ethscriptions_protocol_CreateEthscription(
        address indexed initialOwner,
        string contentURI
    );

    constructor() {
        _init();
        fee = 0.001 ether;
    }

    receive() external payable {}

    function withdraw() external onlyOwner {
        (bool success, ) = (msg.sender).call{value: address(this).balance }("");
        require(success);
    }

    function mint() external payable {
        require(msg.value >= fee);
        _mint(msg.sender);
    }

    function mintTo(address _to) external onlyOwner {
        _mint(_to);
    }

    function setFee(uint256 _fee) external onlyOwner {
        fee = _fee;
    }

    function _mint(address _to) internal {
        uint256 seed = uint256(keccak256(abi.encodePacked(block.number, _to, totalSupply)));
        
        string memory data = _generateSVG(
            backgroundColours[seed % backgroundColours.length],
            faceColours[seed % faceColours.length],
            hatColours[seed % hatColours.length],
            neutralColours[seed % neutralColours.length]
        );

        totalSupply++;
        emit ethscriptions_protocol_CreateEthscription(_to, string.concat('data:image/svg+xml;base64,', Base64.encode(bytes(data))));
    }

    function _generateSVG(
        string memory _backgroundColour,
        DoubleString memory _faceColours,
        TripleString memory _hatColours,
        DoubleString memory _neutralColours
    ) internal view returns (string memory) {
        string memory svgHTML0 = string.concat('<svg xmlns="http://www.w3.org/2000/svg" preserveAspectRatio="xMinYMin meet" viewBox="0 0 240 240"><style id="', Strings.toString(totalSupply), '"/><rect width="100%" height="100%" fill="', _backgroundColour, '" /><polygon points="200,160 200,70 180,70 180,60 60,60 60,160" fill="', _hatColours.light, '"/><rect width="10.1" height="10" x="20" y="170" fill="', _faceColours.dark, '"/><rect width="10" height="10.1" x="40" y="150" fill="', _faceColours.dark);
        svgHTML0 = string.concat(svgHTML0, '"/><polygon points="30,160 50,160 50,180 60,180 60,190 70,190 70,180 80,180 80,200 50,200 50,190 40,190 40,180 30,180" fill="', _neutralColours.dark,'"/><polygon points="70,180 70,190 60,190 60,180 50,180 50,160 60,160 60,150 70,150" fill="', _neutralColours.light, '"/><rect width="10" height="10" x="60" y="170" fill="', _faceColours.dark, '"/><rect width="10" height="10" x="60" y="160" fill="', _faceColours.light);
        
        string memory svgHTML1 = string.concat('"/><rect width="10.1" height="10.1" x="59.95" y="229.95" fill="', _faceColours.dark, '"/><polygon points="70,240 170,240 170,160 70,160 70,180 80,180 80,220 70,220" fill="', _neutralColours.light, '"/><polygon points="90,210 90,200 80,200 80,220 60,220 60,240 50,240 50,230 70,230 70,210" fill="', _neutralColours.dark,'"/><rect width="10" height="10" x="110" y="220" fill="', _faceColours.dark);
        svgHTML1 = string.concat(svgHTML1, '"/><polygon points="90,210 110,210 110,230 100,230 100,220 90,220" fill="', _neutralColours.dark, '"/><polygon points="110,220 170,220 170,200 180,200 180,170 110,170 110,180 100,180 100,200 110,200" fill="', _faceColours.light, '"/><polygon points="120,220 150,220 150,230 140,230 140,240 130,240 130,230 120,230" fill="', _neutralColours.dark, '"/><rect width="10" height="10" x="120" y="200" fill="', _neutralColours.dark);
        
        string memory svgHTML2 = string.concat('"/><polygon points="130,210 130,200 140,200 140,220 150,220 150,210" fill="', _faceColours.dark, '"/><rect width="10.1" height="10" x="179.9" y="230" fill="', _faceColours.dark, '"/><polygon points="150,220 150,210 170,210 170,240 180,240 180,220" fill="', _neutralColours.dark, '"/><rect width="10" height="10" x="160" y="200" fill="', _faceColours.dark);
        svgHTML2 = string.concat(svgHTML2, '"/><polygon points="170,200 170,210 180,210 180,180 160,180 160,160 130,160 130,170 200,170 200,70 190,70 190,90 210,90 210,120 190,120 190,150 210,150 210,180 190,180 190,200" fill="', _neutralColours.dark, '"/><rect width="20.1" height="30.1" x="59.95" y="89.95" fill="', _hatColours.medium, '"/><polygon points="59,120 59,141 90,141 90,130 110,130 110,110 140,110 140,130 170,130 170,120 90,120 90,100 100,100 100,60 90,60 90,90 80,90 80,110 70,110 70,120" fill="', _hatColours.dark, '"/><polygon points="50,160 50,90 60,90 60,140 100,140 100,180 90,180 90,160 120,160 120,150 80,150 80,160 70,160 70,150 60,150 60,160" fill="', _neutralColours.dark);
        
        string memory svgHTML3 = string.concat('"/><rect width="20.1" height="10.1" x="79.95" y="149.95" fill="', _faceColours.dark, '"/><rect width="20" height="10.1" x="110" y="159.95" fill="', _faceColours.dark, '"/><polygon points="130,180 140,180 140,190 150,190 150,180 160,180 160,170 130,170" fill="', _faceColours.dark, '"/><rect width="10" height="10.1" x="50" y="79.95" fill="', _hatColours.dark);
        svgHTML3 = string.concat(svgHTML3, '"/><rect width="10.1" height="10.1" x="59.95" y="69.95" fill="', _neutralColours.dark, '"/><rect width="10.1" height="10.1" x="59.95" y="59.95" fill="', _hatColours.dark, '"/><rect width="50" height="20" x="90" y="40" fill="', _hatColours.dark, '"/><rect width="20.1" height="10" x="69.95" y="50" fill="', _neutralColours.dark);
        
        string memory svgHTML4 = string.concat('"/><rect width="10" height="10" x="90" y="50" fill="', _hatColours.medium, '"/><rect width="30" height="10" x="100" y="40" fill="', _neutralColours.dark, '"/><rect width="10" height="20" x="160" y="50" fill="', _hatColours.dark, '"/><rect width="20.1" height="10" x="139.95" y="50" fill="', _neutralColours.dark);
        svgHTML4 = string.concat(svgHTML4, '"/><rect width="10.1" height="10" x="169.95" y="60" fill="', _neutralColours.dark, '"/><rect width="10.1" height="20" x="179.95" y="60" fill="', _hatColours.dark, '"/><rect width="10.1" height="10.1" x="189.95" y="89.95" fill="', _hatColours.dark, '"/><rect width="20.1" height="10" x="169.95" y="130" fill="', _hatColours.dark);
        
        return string.concat(svgHTML0, svgHTML1, svgHTML2, svgHTML3, svgHTML4, '"/><polygon points="160,60 150,60 150,120 140,120 140,100 160,100" fill="', _hatColours.medium, '"/><polygon points="100,130 90,130 90,140 120,140 120,160 200,160 200,170 160,170 160,150 100,150" fill="', _hatColours.medium, '"/></svg>');
    }

    function _init() internal {
        _storeBackgroundColours();
        _storeFaceColours();
        _storeHatColours();
        _storeNeutralColours();
    }

    function _storeBackgroundColours() internal {
        backgroundColours.push("#fff8dc");
        backgroundColours.push("#dbc9c9");
        backgroundColours.push("#84b4d0");
        backgroundColours.push("#d0a7c7");
        backgroundColours.push("#80ebeb");
        backgroundColours.push("#dee5e5");
        backgroundColours.push("#efcd76");
        backgroundColours.push("#ed8f90");
        backgroundColours.push("#747470");
        backgroundColours.push("#69a975");
        backgroundColours.push("#8467a9");
        backgroundColours.push("#df6cc3");
        backgroundColours.push("#f18c51");
        backgroundColours.push("#1fc29f");
        backgroundColours.push("#79916f");
        backgroundColours.push("#cf5108");
        backgroundColours.push("#a11C06");
        backgroundColours.push("#280575");
        backgroundColours.push("#348505");
        backgroundColours.push("#b20560");
        backgroundColours.push("#057eb2");
        backgroundColours.push("#3F3F3F");
        backgroundColours.push("#DCB40E");
    }

    function _storeFaceColours() internal {
        DoubleString memory _faceColours0 = DoubleString({
            light: "#896bef",
            dark: "#2d0ba7"
        });
        DoubleString memory _faceColours1 = DoubleString({
            light: "#68bee1",
            dark: "#0b7ba7"
        });
        DoubleString memory _faceColours2 = DoubleString({
            light: "#c8a968",
            dark: "#775303"
        });
        DoubleString memory _faceColours3 = DoubleString({
            light: "#6475b8",
            dark: "#082084"
        });
        DoubleString memory _faceColours4 = DoubleString({
            light: "#9d95a5",
            dark: "#48444d"
        });
        DoubleString memory _faceColours5 = DoubleString({
            light: "#499568",
            dark: "#025524"
        });
        DoubleString memory _faceColours6 = DoubleString({
            light: "#af60a2",
            dark: "#5b014a"
        });
        DoubleString memory _faceColours7 = DoubleString({
            light: "#eb885e",
            dark: "#8e2c02"
        });
        DoubleString memory _faceColours8 = DoubleString({
            light: "#d55d6b",
            dark: "#8e0214"
        });
        DoubleString memory _faceColours9 = DoubleString({
            light: "#ac74df",
            dark: "#500095"
        });
        DoubleString memory _faceColours10 = DoubleString({
            light: "#e371b3",
            dark: "#99085d"
        });
        DoubleString memory _faceColours11 = DoubleString({
            light: "#71a59a",
            dark: "#044d41"
        });
        DoubleString memory _faceColours12 = DoubleString({
            light: "#f4d963",
            dark: "#b99500"
        });

        faceColours.push(_faceColours0);
        faceColours.push(_faceColours1);
        faceColours.push(_faceColours2);
        faceColours.push(_faceColours3);
        faceColours.push(_faceColours4);
        faceColours.push(_faceColours5);
        faceColours.push(_faceColours6);
        faceColours.push(_faceColours7);
        faceColours.push(_faceColours8);
        faceColours.push(_faceColours9);
        faceColours.push(_faceColours10);
        faceColours.push(_faceColours11);
        faceColours.push(_faceColours12);
    }

    function _storeHatColours() internal {
        TripleString memory _hatColours0 = TripleString({
            light: "#f8869d",
            medium: "#dc143c",
            dark: "#740e23"
        });
        TripleString memory _hatColours1 = TripleString({
            light: "#635ab5",
            medium: "#2717ed",
            dark: "#100880"
        });
        TripleString memory _hatColours2 = TripleString({
            light: "#e576ed",
            medium: "#e216f1",
            dark: "#870891"
        });
        TripleString memory _hatColours3 = TripleString({
            light: "#79e178",
            medium: "#0eb80c",
            dark: "#025d01"
        });
        TripleString memory _hatColours4 = TripleString({
            light: "#e39f4f",
            medium: "#dc7a05",
            dark: "#a35903"
        });
        TripleString memory _hatColours5 = TripleString({
            light: "#5acfea",
            medium: "#05b4d5",
            dark: "#03819a"
        });
        TripleString memory _hatColours6 = TripleString({
            light: "#69dfa0",
            medium: "#13cc69",
            dark: "#008c3e"
        });
        TripleString memory _hatColours7 = TripleString({
            light: "#a5a5a8",
            medium: "#6f6f73",
            dark: "#3d3d3f"
        });
        TripleString memory _hatColours8 = TripleString({
            light: "#a55454",
            medium: "#af0c0c",
            dark: "#610303"
        });
        TripleString memory _hatColours9 = TripleString({
            light: "#745473",
            medium: "#9b0297",
            dark: "#4d004b"
        });
        TripleString memory _hatColours10 = TripleString({
            light: "#f4d963",
            medium: "#f8cb04",
            dark: "#c19C00"
        });

        hatColours.push(_hatColours0);
        hatColours.push(_hatColours1);
        hatColours.push(_hatColours2);
        hatColours.push(_hatColours3);
        hatColours.push(_hatColours4);
        hatColours.push(_hatColours5);
        hatColours.push(_hatColours6);
        hatColours.push(_hatColours7);
        hatColours.push(_hatColours8);
        hatColours.push(_hatColours9);
        hatColours.push(_hatColours10);
    }

    function _storeNeutralColours() internal {
        DoubleString memory _neutralColours0 = DoubleString({
            light: "#cfc497",
            dark: "#000000"
        });
        DoubleString memory _neutralColours1 = DoubleString({
            light: "#969176",
            dark: "#000000"
        });
        DoubleString memory _neutralColours2 = DoubleString({
            light: "#756c59",
            dark: "#000000"
        });

        neutralColours.push(_neutralColours0);
        neutralColours.push(_neutralColours1);
        neutralColours.push(_neutralColours2);
    }
}
// File: lib/openzeppelin-contracts/contracts/utils/Base64.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Base64.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides a set of functions to operate with Base64 strings.
 *
 * _Available since v4.5._
 */
library Base64 {
    /**
     * @dev Base64 Encoding/Decoding Table
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";

    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal 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 "";

        // Loads the table into memory
        string memory table = _TABLE;

        // Encoding takes 3 bytes chunks of binary data from `bytes` data parameter
        // and split into 4 numbers of 6 bits.
        // The final Base64 length should be `bytes` data length multiplied by 4/3 rounded up
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        // - `4 *`              -> 4 characters for each chunk
        string memory result = new string(4 * ((data.length + 2) / 3));

        /// @solidity memory-safe-assembly
        assembly {
            // Prepare the lookup table (skip the first "length" byte)
            let tablePtr := add(table, 1)

            // Prepare result pointer, jump over length
            let resultPtr := add(result, 32)

            // Run over the input, 3 bytes at a time
            for {
                let dataPtr := data
                let endPtr := add(data, mload(data))
            } lt(dataPtr, endPtr) {

            } {
                // Advance 3 bytes
                dataPtr := add(dataPtr, 3)
                let input := mload(dataPtr)

                // To write each character, shift the 3 bytes (18 bits) chunk
                // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
                // and apply logical AND with 0x3F which is the number of
                // the previous character in the ASCII table prior to the Base64 Table
                // The result is then added to the table to get the character to write,
                // and finally write it in the result pointer but with a left shift
                // of 256 (1 byte) - 8 (1 ASCII char) = 248 bits

                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
            }

            // 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;
    }
}

// File: lib/openzeppelin-contracts/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// File: lib/openzeppelin-contracts/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

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

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

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

// File: contracts/interfaces/ICookiStructs.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.21;

interface ICookiStructs {
    struct DoubleString {
        string light;
        string dark;
    }

    struct TripleString {
        string light;
        string medium;
        string dark;
    }
}
// File: lib/openzeppelin-contracts/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

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

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

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

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// File: lib/openzeppelin-contracts/contracts/utils/math/SignedMath.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

// File: lib/openzeppelin-contracts/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

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