// File: src/TokenURI.sol



// SPDX-License-Identifier: MIT
// TokenURI Contracts v0.0.1
// Creator: RockArt 🪨 AI

pragma solidity ^0.8.20;

import { Strings } from "openzeppelin/utils/Strings.sol";
import { Base64 } from "openzeppelin/utils/Base64.sol";

interface ITokenURI {
    function setToken(
        address from,
        uint256 tokenId
    ) external;

    function tokenURI(
        uint256 tokenId
    ) external view returns (string memory);
}

contract TokenURI is ITokenURI {
    using Strings for uint256;

    address public nft;
    address public owner;

    string private _description = string(abi.encodePacked(
        unicode'[ BUY = +1 of 6 ] ⇢ [ lost 🔴 | 🟢 win ] ⇢ [ SELL = +1 of 6 ]',
        unicode' ❗️ Attention ❗️ to add cartridge you need',
        unicode' ⚪️ 👉 Sell for native token (ETH)',
        unicode' ⚪️ 👉 Buy one token in one transaction (1 token in cart)',
        unicode' ⚪️ 👉 Use only marketplace Opensea'
    ));

    address[] private _markets;

    uint256 public memberId;
    mapping(uint256 => uint256) public memberToken;
    mapping(uint256 => uint256) public tokenMember;
    mapping(uint256 => uint256) public drum;
    mapping(uint256 => uint256) public color;

    string[16] private _mascot = [
        unicode"🐶", unicode"🐱", unicode"🐭", unicode"🐹",
        unicode"🐰", unicode"🦊", unicode"🐻", unicode"🐼",
        unicode"🐻‍❄️", unicode"🐨", unicode"🐯", unicode"🦁",
        unicode"🐮", unicode"🐷", unicode"🐸", unicode"🐵"
    ];

    string[6] private _cx = ["71.6", "71.6", "50", "28.5", "28.5", "50"];
    string[6] private _cy = ["37.5", "62.6", "75", "62.6", "37.5", "25"];
    string[3] private _r = ["9", "6", "5"];
    string[3] private _red = ["cc0000", "bb0000", "dd0000"];

    modifier onlyNft {
        require(msg.sender == nft, "Only NFT contract");
        _;
    }

    modifier onlyOwner {
        require(msg.sender == owner, "Only Owner user");
        _;
    }

    constructor(address nft_) {
        nft = nft_;
        owner = msg.sender;
    }

    function setToken(
        address from,
        uint256 tokenId
    ) external onlyNft {
        if (from == address(0) || _isSale()) {
            if (color[tokenId] <= 0) {
                uint256 r = uint256(keccak256(abi.encodePacked(
                    block.number,
                    block.prevrandao,
                    tokenId
                )));
                color[tokenId] = r > type(uint128).max
                    ? r
                    : r + type(uint128).max;
            } else {
                (uint256 c, uint256 r) = _parse(tokenId);
                if (r == 0 || (c < 5 && c < r)) {
                    c += 1;
                    r = (uint256(keccak256(abi.encodePacked(
                        block.number,
                        block.prevrandao,
                        tokenId
                    )))) % 6 + 1;
                    drum[tokenId] = (c * 10) + r;
                    if (c == 5 && r == 6) {
                        memberId += 1;
                        memberToken[memberId] = tokenId;
                        tokenMember[tokenId] = memberId;
                    }
                }
            }
        }
    }

    function setDescription(string memory description_) public onlyOwner {
        _description = description_;
    }

    function addMarket(address[] memory markets_) public onlyOwner {
        for (uint256 i = 0; i < markets_.length; i++) {
            _markets.push(markets_[i]);
        }
    }

    function delMarket(address[] memory markets_) public onlyOwner {
        for (uint256 i = 0; i < _markets.length; i++) {
            for (uint256 j = 0; j < markets_.length; j++) {
                address market = markets_[j];
                if (market == _markets[i]) {
                    _markets[i] = _markets[_markets.length-1];
                    _markets.pop();
                    break;
                }
            }
        }
    }

    function _isSale() private view returns (bool sale) {
        for (uint256 i = 0; i < _markets.length; i++) {
            if (address(_markets[i]).balance > 0) {
                sale = true;
                break;
            }
        }
    }

    function tokenURI(
        uint256 tokenId
    ) public view virtual returns (string memory) {
        return string(abi.encodePacked(
            'data:application/json;utf8,',
            abi.encodePacked(
                '{',
                    '"name":"', _name(tokenId),
                    '","description":"', _description,
                    '","external_url":"https://6of6club.eth.limo',
                    '","background_color":"', backgroundColor(tokenId),
                    '","attributes":', _attributes(tokenId),
                    ',"image":"', _image(tokenId),
                '"}'
            )
        ));
    }

    function _parse(
        uint256 tokenId
    ) private view returns (uint256 c, uint256 r) {
        c = uint256(drum[tokenId]) / uint256(10);
        r = uint256(drum[tokenId]) % uint256(10);
    }

    function _name(
        uint256 tokenId
    ) private view returns (string memory) {
        (uint256 c, uint256 r) = _parse(tokenId);

        return string(abi.encodePacked(
            (r == 6 && c == 5 ? 6 : c).toString(),
            'of6 Club #',
            tokenId.toString()
        ));
    }

    function _image(
        uint256 tokenId
    ) private view returns (string memory) {
        (uint256 c, uint256 r) = _parse(tokenId);

        uint256 cartridgeRed = (color[tokenId] % 10**3) % 86 + 1;
        uint256 cartridgeGreen = ((color[tokenId] / 10**3) % 10**3) % 221 + 1;
        uint256 cartridgeBlue = ((color[tokenId] / 10**6) % 10**3) % 221 + 1;

        string[3] memory fill = [
            _rgbToHex(
                cartridgeRed + 17,
                cartridgeGreen + 17,
                cartridgeBlue + 17
            ),
            _rgbToHex(
                cartridgeRed,
                cartridgeGreen,
                cartridgeBlue
            ),
            _rgbToHex(
                cartridgeRed + 34,
                cartridgeGreen + 34,
                cartridgeBlue + 34
            )
        ];

        return string(abi.encodePacked(
            'data:image/svg+xml;base64,',
            Base64.encode(abi.encodePacked(
                '<svg viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg"><defs>',
                _radialGradient(tokenId),
                _style(tokenId),
                '</defs>',
                (c > 0 ? _cartridges(c, fill) : bytes('')),
                (r > 0 ? _cartridge(r, c < r ? fill : _red) : bytes('')),
                '<path d="m88.408 38.831c-1.823-6.278-5.14-11.916-9.545-16.508-3.834 0.265-7.785-0.568-11.363-2.634-3.583-2.069-6.283-5.079-7.97-8.537-3.055-0.747-6.245-1.152-9.53-1.152s-6.475 0.405-9.53 1.152c-1.687 3.459-4.387 6.469-7.97 8.537-3.578 2.066-7.529 2.899-11.363 2.634-4.405 4.592-7.722 10.23-9.545 16.508 2.151 3.189 3.408 7.032 3.408 11.169s-1.257 7.98-3.408 11.169c1.823 6.278 5.14 11.916 9.545 16.508 3.834-0.265 7.785 0.568 11.363 2.634 3.583 2.069 6.283 5.079 7.97 8.538 3.055 0.746 6.245 1.151 9.53 1.151s6.475-0.405 9.53-1.152c1.687-3.459 4.387-6.469 7.97-8.538 3.578-2.066 7.529-2.899 11.363-2.634 4.405-4.592 7.722-10.23 9.545-16.508-2.151-3.188-3.408-7.031-3.408-11.168s1.257-7.98 3.408-11.169zm-25.417-6.331c2.761-4.783 8.877-6.421 13.659-3.66 4.783 2.761 6.421 8.877 3.66 13.659-2.761 4.783-8.877 6.421-13.659 3.66-4.783-2.761-6.421-8.877-3.66-13.659zm-25.984 35c-2.761 4.783-8.877 6.421-13.659 3.66-4.783-2.761-6.421-8.877-3.66-13.659 2.761-4.783 8.877-6.421 13.659-3.66 4.783 2.761 6.422 8.876 3.66 13.659zm-8.659-20.001c-5.522 0-9.999-4.477-9.999-9.999s4.477-9.999 9.999-9.999 9.999 4.477 9.999 9.999-4.477 9.999-9.999 9.999zm26.651 36.161c-4.783 2.762-10.898 1.123-13.659-3.66s-1.123-10.898 3.66-13.659 10.898-1.123 13.659 3.66 1.122 10.898-3.66 13.659zm-9.999-33.66c0-2.761 2.239-5 5-5s5 2.239 5 5-2.239 5-5 5-5-2.239-5-5zm9.999-16.341c-4.783 2.761-10.898 1.123-13.659-3.66-2.762-4.783-1.123-10.898 3.66-13.659s10.898-1.123 13.659 3.66c2.761 4.782 1.122 10.897-3.66 13.659zm16.652 38.841c-5.522 0-9.999-4.477-9.999-9.999s4.477-9.999 9.999-9.999 9.999 4.477 9.999 9.999-4.477 9.999-9.999 9.999z" fill="url(#a)"></path>',
                (r == 6 && c == 5 ? _mascotFor(tokenId) : bytes('')),
                '</svg>'
            ))
        ));
    }

    function _radialGradient(
        uint256 tokenId
    ) private view returns (bytes memory) {
        (string memory start, string memory stop) = gradientColor(tokenId);

        return abi.encodePacked(
            '<radialGradient id="a"><stop stop-color="#',
            start,
            '" offset="0"/><stop stop-color="#',
            stop,
            '" offset="1"/></radialGradient>'
        );
    }

    function _style(
        uint256 tokenId
    ) private view returns (bytes memory) {
        (uint256 c, uint256 r) = _parse(tokenId);

        return abi.encodePacked(
            '<style><![CDATA[svg{overflow:hidden;background:#',
            backgroundColor(tokenId),
            ';animation:5s ease-in-out 1s forwards r}@keyframes r{0%{transform:rotateZ(0)}100%{transform:rotateZ(',
            (1800 - 60 * r).toString(),
            'deg)}}circle:nth-of-type(-n+3){opacity:0;animation:1s ease-in-out forwards f}circle:nth-last-of-type(-n+3){opacity:0;', 
            (r <= c || c == 5 ? 'animation:1s ease-in-out 6s forwards f' : ''),
            '}text{opacity:0;', 
            (r == 6 && c == 5 ? 'animation:1s ease-in-out 6s forwards f' : ''), 
            '}@keyframes f{0%{opacity:0}100%{opacity:1}}]]></style>'
        );
    }

    function _mascotFor(
        uint256 tokenId
    ) private view returns (bytes memory) {
        (, uint256 r) = _parse(tokenId);

        return abi.encodePacked(
            '<text x="50%" y="50%" dominant-baseline="central" text-anchor="middle" style="font-size: 20px;" transform="rotate(',
            (60 * r).toString(),
            ', 50, 50)">',
            _mascot[uint256(color[tokenId] % 16)],
            '</text>'
        );
    }

    function _cartridges(
        uint256 max,
        string[3] memory fill
    ) private view returns (bytes memory) {
        bytes memory result;
        for (uint256 i = max; i >= 1; i--) {
            result = abi.encodePacked(
                result,
                _cartridge(i, fill)
            );
        }
        return result;
    }

    function _cartridge(
        uint256 position,
        string[3] memory fill
    ) private view returns (bytes memory) {
        return abi.encodePacked(
            _circle(_cx[position - 1], _cy[position - 1], _r[0], fill[0]),
            _circle(_cx[position - 1], _cy[position - 1], _r[1], fill[1]),
            _circle(_cx[position - 1], _cy[position - 1], _r[2], fill[2])
        );
    }

    function _circle(
        string memory cx,
        string memory cy,
        string memory r,
        string memory fill
    ) private pure returns (bytes memory) {
        return abi.encodePacked(
            '<circle cx="', cx,
            '" cy="', cy,
            '" r="', r,
            '" fill="#', fill,
            '"></circle>'
        );
    }

    function _attributes(
        uint256 tokenId
    ) private view returns (bytes memory) {
        return abi.encodePacked(
            '[{"trait_type": "CARTRIDGES", "value": "',
            _typeCartridges(tokenId), '"},',
            '{"trait_type": "MASCOT", "value": "',
            _typeMascot(tokenId), '"},',
            '{"trait_type": "MEMBER ID", "value": "', 
            _typeMemberId(tokenId), '"}]'
        );
    }

    function _typeCartridges(
        uint256 tokenId
    ) private view returns (bytes memory cs) {
        (uint256 c, uint256 r) = _parse(tokenId);

        bool q;
        for (uint256 i = 1; i <= 6; i++) {
            if (i <= c) {
                if (i == c && r <= c) {
                    cs = abi.encodePacked(cs, unicode"🔴");
                    q = true;
                } else {
                    cs = abi.encodePacked(cs, unicode"🟢");
                }
            } else {
                if (q) {
                    cs = abi.encodePacked(cs, unicode"⚪️");
                } else {
                    if (c == 5 && r == 6) {
                        cs = abi.encodePacked(cs, unicode"🟢");
                    } else {
                        cs = abi.encodePacked(cs, unicode"❔");
                        q = true;
                    }
                }
            }
        }
    }

    function _typeMascot(
        uint256 tokenId
    ) private view returns (string memory) {
        (uint256 c, uint256 r) = _parse(tokenId);

        return c > 0 && c >= r
            ? unicode"🔴"
            : r == 6 && c == 5
                ? _mascot[uint256(color[tokenId] % 16)]
                : unicode"❔";
    }

    function _typeMemberId(
        uint256 tokenId
    ) private view returns (string memory) {
        (uint256 c, uint256 r) = _parse(tokenId);

        return r == 6 && c == 5
            ? (tokenMember[tokenId]).toString() 
            : "Non-member";
    }

    function clubMember(
        uint64 id
    ) public view returns (string memory) {
        require(memberToken[id] > 0);
        return tokenURI(memberToken[id]);
    }

    function _rgbToHex(
        uint256 r,
        uint256 g,
        uint256 b
    ) private pure returns (string memory) {
        uint256 decimalValue = (r << 16) | (g << 8) | b;
        uint256 remainder;
        bytes memory hexResult = "";
        string[16] memory hexDictionary = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F"];

        while (decimalValue > 0) {
            remainder = decimalValue % 16;
            string memory hexValue = hexDictionary[remainder];
            hexResult = abi.encodePacked(hexValue, hexResult);
            decimalValue = decimalValue / 16;
        }
        
        uint len = hexResult.length;

        if (len == 5) {
            hexResult = abi.encodePacked("0", hexResult);
        } else if (len == 4) {
            hexResult = abi.encodePacked("00", hexResult);
        } else if (len == 3) {
            hexResult = abi.encodePacked("000", hexResult);
        } else if (len == 4) {
            hexResult = abi.encodePacked("0000", hexResult);
        }

        return string(hexResult);
    }

    function backgroundColor(
        uint256 tokenId
    ) public view returns (string memory) {
        return _rgbToHex(
            ((color[tokenId] / 10**9) % 10**3) % 100 + 1,
            ((color[tokenId] / 10**12) % 10**3) % 100 + 1,
            ((color[tokenId] / 10**15) % 10**3) % 100 + 1
        );
    }

    function gradientColor(
        uint256 tokenId
    ) public view returns (string memory, string memory) {
        uint256 cartridgeRed = (color[tokenId] % 10**3) % 86 + 1;
        uint256 cartridgeGreen = ((color[tokenId] / 10**3) % 10**3) % 221 + 1;
        uint256 cartridgeBlue = ((color[tokenId] / 10**6) % 10**3) % 221 + 1;

        return (
            _rgbToHex(
                cartridgeRed + cartridgeRed % 34,
                cartridgeGreen + cartridgeGreen % 34,
                cartridgeBlue + cartridgeBlue % 34
            ),
            _rgbToHex(
                ((color[tokenId] / 10**18) % 10**3) % 155 + 100,
                ((color[tokenId] / 10**21) % 10**3) % 155 + 100,
                ((color[tokenId] / 10**24) % 10**3) % 155 + 100
            )
        );
    }
}

// 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/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/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);
        }
    }
}