// File: contracts/AnnoOxypetalum.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @artist: Anna Ridler
/// @author: manifold.xyz

import "@prb/math/contracts/PRBMathSD59x18.sol";
import "./libraries/Trigonometry.sol";
import "./libraries/BokkyPooBahsDateTimeLibrary.sol";

import "./dynamic/DynamicArweaveHash.sol";
import "./extensions/ERC721/IERC721CreatorExtensionApproveTransfer.sol";

contract AnnoOxypetalum is DynamicArweaveHash, IERC721CreatorExtensionApproveTransfer {
    using PRBMathSD59x18 for int256;

    uint256 private _baseTokenId;
    uint8 private _seasonOnLastTransfer;

    // Seasons
    uint8 constant private _WINTER = 0;
    uint8 constant private _SPRING = 1;
    uint8 constant private _SUMMER = 2;
    uint8 constant private _FALL = 3;
    
    // Constants
    int256 constant private _DAY_IN_SECONDS = 86400000000000000000000;
    int256 constant private _JULIAN_EPOCH = 2440587500000000000000000;
    int256 constant private _JULIAN_2000 = 2451545000000000000000000;
    int256 constant private _JULIAN_CENTURY = 36525000000000000000000;
    
    int256 immutable _D2R = PRBMathSD59x18.pi().div(180000000000000000000);

    // In-memory Arrays
    function _springConstants() private pure returns (int256[5] memory) {
        int256[5] memory constants = 
            [int(2451623809840000000000000), 
            365242374040000000000000, 
            51690000000000000, 
            -4110000000000000, 
            -570000000000000];
        return constants;
    }

    function _summerConstants() private pure returns (int256[5] memory) {
        int256[5] memory constants = 
            [int(2451716567670000000000000), 
            365241626030000000000000, 
            3250000000000000, 
            8880000000000000, 
            -300000000000000];
        return constants;
    }

    function _fallConstants() private pure returns (int256[5] memory) {
        int256[5] memory constants = 
            [int(2451810217150000000000000),
            365242017670000000000000,
            -115750000000000000,
            3370000000000000,
            780000000000000];
        return constants;
    }

    function _winterConstants() private pure returns (int256[5] memory) {
        int256[5] memory constants = 
            [int(2451900059520000000000000),
            365242740490000000000000,
            -62230000000000000,
            -8230000000000000,
            320000000000000];
        return constants;
    }

    function _termsConstants() private pure returns (int256[3][24] memory) {
        int256[3][24] memory constants = 
            [
                [int(485000000000000000000), 324960000000000000000, 1934136000000000000000],
                [int(203000000000000000000), 337230000000000000000, 32964467000000000000000],
                [int(199000000000000000000), 342080000000000000000, 20186000000000000000],
                [int(182000000000000000000), 27850000000000000000, 445267112000000000000000],
                [int(156000000000000000000), 73140000000000000000, 45036886000000000000000],
                [int(136000000000000000000), 171520000000000000000, 22518443000000000000000],
                [int(77000000000000000000), 222540000000000000000, 65928934000000000000000],
                [int(74000000000000000000), 296720000000000000000, 3034906000000000000000],
                [int(70000000000000000000), 243580000000000000000, 9037513000000000000000],
                [int(58000000000000000000), 119810000000000000000, 33718147000000000000000],
                [int(52000000000000000000), 297170000000000000000, 150678000000000000000],
                [int(50000000000000000000), 21020000000000000000, 2281226000000000000000],
                [int(45000000000000000000), 247540000000000000000, 29929562000000000000000],
                [int(44000000000000000000), 325150000000000000000, 31555956000000000000000],
                [int(29000000000000000000), 60930000000000000000, 4443417000000000000000],
                [int(18000000000000000000), 155120000000000000000, 67555328000000000000000],
                [int(17000000000000000000), 288790000000000000000, 4562452000000000000000],
                [int(16000000000000000000), 198040000000000000000, 62894029000000000000000],
                [int(14000000000000000000), 199760000000000000000, 31436921000000000000000],
                [int(12000000000000000000), 95390000000000000000, 14577848000000000000000],
                [int(12000000000000000000), 287110000000000000000, 31931756000000000000000],
                [int(12000000000000000000), 320810000000000000000, 34777259000000000000000],
                [int(9000000000000000000), 227730000000000000000, 1222114000000000000000],
                [int(8000000000000000000), 15450000000000000000, 16859074000000000000000]
            ];
        return constants;
    }

    constructor(address creator) ERC721SingleCreatorExtension(creator) {}

    function supportsInterface(bytes4 interfaceId) public view virtual override(DynamicArweaveHash, IERC165) returns (bool) {
        return interfaceId == type(IERC721CreatorExtensionApproveTransfer).interfaceId || super.supportsInterface(interfaceId);
    }

    function mint(address to) public virtual onlyOwner returns(uint256) {
        require(_baseTokenId == 0, "Already minted");
        _baseTokenId = _mint(to);
        return _baseTokenId;
    }

    function setApproveTransfer(address creator, bool enabled) public override onlyOwner {
        IERC721CreatorCore(creator).setApproveTransferExtension(enabled);
    }

    function approveTransfer(address, address, uint256) public override returns (bool) {
        require(msg.sender == _creator, "Invalid requester");
        _seasonOnLastTransfer = _currentSeason();
        return true;
    }

    function tokenURI(address, uint256 tokenId) external view override returns (string memory) {
        return string(abi.encodePacked(
            'data:application/json;utf8,{"name":"',_getName(),
                                         '", "description":"',_getDescription(),
                                         '", "image":"https://arweave.net/',_getImageHash(tokenId),
                                         '", "animation_url":"https://arweave.net/',_getAnimationHash(tokenId),
                                         '", "attributes":[',
                                            _wrapTrait("Artist", "Anna Ridler"),
                                         ']',
                                         '}'));
    }


    function _getName() internal pure override returns(string memory) {
        return "Anno oxypetalum";
    }

    function _getDescription() internal pure override returns(string memory) {
        return 
            "Anno oxypetalum (literally \\\"the year of the pointed petals\\\") is a clock made of the flowers of "
            "night-blooming cacti, tracking the amount of light across one year. Each flower represents 10 minutes, "
            "each second approximately 2 days. Over the course of the piece the flowers fade in and out as the light "
            "ebbs and flows across the seasons. The timing of dawn and dusk is precisely accurate for London starting "
            "at the 2021 winter solstice. A third level of time is also incorporated into the work - when the piece "
            "is sold, the smart contract is programmed to start the video at the beginning of the season in which it "
            "was sold. The smart contract is able to accurately compute the solstices and equinoxes until the year "
            "3000. It is inspired by plants\' chrono-biological clocks, by which they bloom and close at fixed times "
            "of day. Plants behave this way regardless of external stimuli -  a night-blooming cactus, for example, "
            "will only bloom at night, even if it is exposed to darkness during the daytime and light at night; a "
            "morning glory moved into permanent darkness will still flower in the mornings. The work call backs to "
            "Carl Linnaeus\' idea of a horologium florae or floral clock, proposed in his Philosophia Botanica in "
            "1751 after observing the phenomenon of certain flowers opening and closing at set times of the day, "
            "and harkens back to an earlier, medieval way of delineating time according to the amount of daylight "
            "present, before the advent of modern timekeeping.";
    }

    function _getImageHash(uint256) internal view override returns(string memory) {
        return imageArweaveHashes[_seasonOnLastTransfer];
    }

    function _getAnimationHash(uint256) internal view override returns(string memory) {
        return animationArweaveHashes[_seasonOnLastTransfer];
    }

    function _wrapTrait(string memory trait, string memory value) internal pure returns(string memory) {
        return string(abi.encodePacked(
            '{"trait_type":"',
            trait,
            '","value":"',
            value,
            '"}'
        ));
    }

    function _currentSeason() private view returns (uint8) {
        int256 year = _timestampToYear(block.timestamp);
        int256 month = _timestampToMonth(block.timestamp);
        int256 julianDay = _timestampToJulianDay(block.timestamp);
        int256[3][24] memory terms = _termsConstants();

        if (month < 3) {
            return _WINTER;
        } else if (month == 3) {
            return julianDay < _springEquinox(year, terms) ? _WINTER : _SPRING;
        } else if (month < 6) {
            return _SPRING;
        } else if (month == 6) {
            return julianDay < _summerSolstice(year, terms) ? _SPRING : _SUMMER;
        } else if (month < 9) {
            return _SUMMER;
        } else if (month == 9) {
            return julianDay < _fallEquinox(year, terms) ? _SUMMER : _FALL;
        } else if (month < 12) {
            return _FALL;
        }
        return julianDay < _winterSolstice(year, terms) ? _FALL : _WINTER;
    }

    function _springEquinox(int256 year, int256[3][24] memory terms) private view returns (int256) {
        return _eventJulianDay(year - 2000000000000000000000, _springConstants(), terms);
    }

    function _summerSolstice(int256 year, int256[3][24] memory terms) private view returns (int256) {
        return _eventJulianDay(year - 2000000000000000000000, _summerConstants(), terms);
    }

    function _fallEquinox(int256 year, int256[3][24] memory terms) private view returns (int256) {
        return _eventJulianDay(year - 2000000000000000000000, _fallConstants(), terms);
    }

    function _winterSolstice(int256 year, int256[3][24] memory terms) private view returns (int256) {
        return _eventJulianDay(year - 2000000000000000000000, _winterConstants(), terms);
    }

    function _eventJulianDay(int256 year, int256[5] memory eventConstants, int256[3][24] memory terms) private view returns (int256) {
        int256 J0 = _horner(year.mul(1000000000000000), eventConstants);
        int256 T = _J2000Century(J0);
        int256 W = _D2R.mul(T).mul(35999373000000000000000) - _D2R.mul(2470000000000000000);
        int256 dL = 1000000000000000000 + Trigonometry.cos(uint(W)).mul(33400000000000000) + Trigonometry.cos(uint(W.mul(2000000000000000000))).mul(700000000000000);
        int256 S = 0;
        for (uint256 i = 24; i > 0; i--) {
            int256[3] memory t = terms[i-1];
            S += t[0].mul(Trigonometry.cos(uint((t[1] + T.mul(t[2])).mul(_D2R))));
        }
        return J0 + S.div(dL).mul(10000000000000);
    }

    function _horner(int256 x, int256[5] memory c) private pure returns (int256) {
        uint256 i = c.length - 1;
        int256 y = c[i];
        while (i > 0) {
            i--;
            y = y.mul(x) + c[i];
        }
        return y;
    }

    function _J2000Century(int256 jde) private pure returns (int256) {
        return (jde - _JULIAN_2000).div(_JULIAN_CENTURY);
    }

     function _timestampToYear(uint256 timestamp) private pure returns (int256) {
        return PRBMathSD59x18.fromInt(int(BokkyPooBahsDateTimeLibrary.getYear(timestamp)));
    }

    function _timestampToMonth(uint256 timestamp) private pure returns (int256) {
        return int(BokkyPooBahsDateTimeLibrary.getMonth(timestamp));
    }

    function _timestampToJulianDay(uint256 timestamp) private pure returns (int256) {
        return PRBMathSD59x18.fromInt(int(timestamp)).div(_DAY_IN_SECONDS) + _JULIAN_EPOCH;
    }
}
// File: contracts/extensions/ERC721/IERC721CreatorExtensionApproveTransfer.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/utils/introspection/IERC165.sol";

/**
 * Implement this if you want your extension to approve a transfer
 */
interface IERC721CreatorExtensionApproveTransfer is IERC165 {

    /**
     * @dev Set whether or not the creator will check the extension for approval of token transfer
     */
    function setApproveTransfer(address creator, bool enabled) external;

    /**
     * @dev Called by creator contract to approve a transfer
     */
    function approveTransfer(address from, address to, uint256 tokenId) external returns (bool);
}

// File: contracts/dynamic/DynamicArweaveHash.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/utils/Strings.sol";

import "@manifoldxyz/creator-core-solidity/contracts/core/IERC721CreatorCore.sol";
import "@manifoldxyz/creator-core-solidity/contracts/extensions/CreatorExtension.sol";
import "@manifoldxyz/creator-core-solidity/contracts/extensions/ICreatorExtensionTokenURI.sol";

import "../libraries/single-creator/ERC721/ERC721SingleCreatorExtension.sol";

/**
 * Extension which allows for the creation of NFTs with dynamically changing image/animation metadata 
 */
abstract contract DynamicArweaveHash is ERC721SingleCreatorExtension, CreatorExtension, Ownable, ICreatorExtensionTokenURI {

    using Strings for uint256;

    string[] public imageArweaveHashes;
    string[] public animationArweaveHashes;

    function supportsInterface(bytes4 interfaceId) public view virtual override(CreatorExtension, IERC165) returns (bool) {
        return interfaceId == type(ICreatorExtensionTokenURI).interfaceId 
        || super.supportsInterface(interfaceId);
    }


    function tokenURI(address, uint256 tokenId) external view virtual override returns (string memory) {
        string memory uri = string(abi.encodePacked('data:application/json;utf8,{"name":"', _getName(), '","description":"', _getDescription()));
        if (imageArweaveHashes.length > 0) {
            uri = string(abi.encodePacked(uri, '", "image":"https://arweave.net/', _getImageHash(tokenId)));
        }
        if (animationArweaveHashes.length > 0) {
            uri = string(abi.encodePacked(uri, '", "animation_url":"https://arweave.net/', _getAnimationHash(tokenId)));
        }
        uri = string(abi.encodePacked(uri, '"}'));
        return uri;
    }

    function _mint(address to) internal returns(uint256) {
        return IERC721CreatorCore(_creator).mintExtension(to);
    }

    function _getName() internal view virtual returns(string memory);

    function _getDescription() internal view virtual returns(string memory);

    function _getImageHash(uint256 tokenId) internal view virtual returns(string memory);

    function _getAnimationHash(uint256 tokenId) internal view virtual returns(string memory);

    function setImageArweaveHashes(string[] memory _arweaveHashes) external virtual onlyOwner {
        imageArweaveHashes = _arweaveHashes;
    }

    function setAnimationAreaveHashes(string[] memory _arweaveHashes) external virtual onlyOwner {
        animationArweaveHashes = _arweaveHashes;
    }
}

// File: contracts/libraries/BokkyPooBahsDateTimeLibrary.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.9.0;

// ----------------------------------------------------------------------------
// BokkyPooBah's DateTime Library v1.01
//
// A gas-efficient Solidity date and time library
//
// https://github.com/bokkypoobah/BokkyPooBahsDateTimeLibrary
//
// Tested date range 1970/01/01 to 2345/12/31
//
// Conventions:
// Unit      | Range         | Notes
// :-------- |:-------------:|:-----
// timestamp | >= 0          | Unix timestamp, number of seconds since 1970/01/01 00:00:00 UTC
// year      | 1970 ... 2345 |
// month     | 1 ... 12      |
// day       | 1 ... 31      |
// hour      | 0 ... 23      |
// minute    | 0 ... 59      |
// second    | 0 ... 59      |
// dayOfWeek | 1 ... 7       | 1 = Monday, ..., 7 = Sunday
//
//
// Enjoy. (c) BokkyPooBah / Bok Consulting Pty Ltd 2018-2019. The MIT Licence.
// ----------------------------------------------------------------------------

library BokkyPooBahsDateTimeLibrary {

    uint constant SECONDS_PER_DAY = 24 * 60 * 60;
    uint constant SECONDS_PER_HOUR = 60 * 60;
    uint constant SECONDS_PER_MINUTE = 60;
    int constant OFFSET19700101 = 2440588;

    uint constant DOW_MON = 1;
    uint constant DOW_TUE = 2;
    uint constant DOW_WED = 3;
    uint constant DOW_THU = 4;
    uint constant DOW_FRI = 5;
    uint constant DOW_SAT = 6;
    uint constant DOW_SUN = 7;

    // ------------------------------------------------------------------------
    // Calculate the number of days from 1970/01/01 to year/month/day using
    // the date conversion algorithm from
    //   https://aa.usno.navy.mil/faq/JD_formula.html
    // and subtracting the offset 2440588 so that 1970/01/01 is day 0
    //
    // days = day
    //      - 32075
    //      + 1461 * (year + 4800 + (month - 14) / 12) / 4
    //      + 367 * (month - 2 - (month - 14) / 12 * 12) / 12
    //      - 3 * ((year + 4900 + (month - 14) / 12) / 100) / 4
    //      - offset
    // ------------------------------------------------------------------------
    function _daysFromDate(uint year, uint month, uint day) internal pure returns (uint _days) {
        require(year >= 1970);
        int _year = int(year);
        int _month = int(month);
        int _day = int(day);

        int __days = _day
          - 32075
          + 1461 * (_year + 4800 + (_month - 14) / 12) / 4
          + 367 * (_month - 2 - (_month - 14) / 12 * 12) / 12
          - 3 * ((_year + 4900 + (_month - 14) / 12) / 100) / 4
          - OFFSET19700101;

        _days = uint(__days);
    }

    // ------------------------------------------------------------------------
    // Calculate year/month/day from the number of days since 1970/01/01 using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // and adding the offset 2440588 so that 1970/01/01 is day 0
    //
    // int L = days + 68569 + offset
    // int N = 4 * L / 146097
    // L = L - (146097 * N + 3) / 4
    // year = 4000 * (L + 1) / 1461001
    // L = L - 1461 * year / 4 + 31
    // month = 80 * L / 2447
    // dd = L - 2447 * month / 80
    // L = month / 11
    // month = month + 2 - 12 * L
    // year = 100 * (N - 49) + year + L
    // ------------------------------------------------------------------------
    function _daysToDate(uint _days) internal pure returns (uint year, uint month, uint day) {
        int __days = int(_days);

        int L = __days + 68569 + OFFSET19700101;
        int N = 4 * L / 146097;
        L = L - (146097 * N + 3) / 4;
        int _year = 4000 * (L + 1) / 1461001;
        L = L - 1461 * _year / 4 + 31;
        int _month = 80 * L / 2447;
        int _day = L - 2447 * _month / 80;
        L = _month / 11;
        _month = _month + 2 - 12 * L;
        _year = 100 * (N - 49) + _year + L;

        year = uint(_year);
        month = uint(_month);
        day = uint(_day);
    }

    function timestampFromDate(uint year, uint month, uint day) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY;
    }
    function timestampFromDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + hour * SECONDS_PER_HOUR + minute * SECONDS_PER_MINUTE + second;
    }
    function timestampToDate(uint timestamp) internal pure returns (uint year, uint month, uint day) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function timestampToDateTime(uint timestamp) internal pure returns (uint year, uint month, uint day, uint hour, uint minute, uint second) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
        secs = secs % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
        second = secs % SECONDS_PER_MINUTE;
    }

    function isValidDate(uint year, uint month, uint day) internal pure returns (bool valid) {
        if (year >= 1970 && month > 0 && month <= 12) {
            uint daysInMonth = _getDaysInMonth(year, month);
            if (day > 0 && day <= daysInMonth) {
                valid = true;
            }
        }
    }
    function isValidDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (bool valid) {
        if (isValidDate(year, month, day)) {
            if (hour < 24 && minute < 60 && second < 60) {
                valid = true;
            }
        }
    }
    function isLeapYear(uint timestamp) internal pure returns (bool leapYear) {
        (uint year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        leapYear = _isLeapYear(year);
    }
    function _isLeapYear(uint year) internal pure returns (bool leapYear) {
        leapYear = ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
    }
    function isWeekDay(uint timestamp) internal pure returns (bool weekDay) {
        weekDay = getDayOfWeek(timestamp) <= DOW_FRI;
    }
    function isWeekEnd(uint timestamp) internal pure returns (bool weekEnd) {
        weekEnd = getDayOfWeek(timestamp) >= DOW_SAT;
    }
    function getDaysInMonth(uint timestamp) internal pure returns (uint daysInMonth) {
        (uint year, uint month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        daysInMonth = _getDaysInMonth(year, month);
    }
    function _getDaysInMonth(uint year, uint month) internal pure returns (uint daysInMonth) {
        if (month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
            daysInMonth = 31;
        } else if (month != 2) {
            daysInMonth = 30;
        } else {
            daysInMonth = _isLeapYear(year) ? 29 : 28;
        }
    }
    // 1 = Monday, 7 = Sunday
    function getDayOfWeek(uint timestamp) internal pure returns (uint dayOfWeek) {
        uint _days = timestamp / SECONDS_PER_DAY;
        dayOfWeek = (_days + 3) % 7 + 1;
    }

    function getYear(uint timestamp) internal pure returns (uint year) {
        (year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getMonth(uint timestamp) internal pure returns (uint month) {
        (,month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getDay(uint timestamp) internal pure returns (uint day) {
        (,,day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getHour(uint timestamp) internal pure returns (uint hour) {
        uint secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
    }
    function getMinute(uint timestamp) internal pure returns (uint minute) {
        uint secs = timestamp % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
    }
    function getSecond(uint timestamp) internal pure returns (uint second) {
        second = timestamp % SECONDS_PER_MINUTE;
    }

    function addYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year += _years;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addMonths(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        month += _months;
        year += (month - 1) / 12;
        month = (month - 1) % 12 + 1;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addDays(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _days * SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _hours * SECONDS_PER_HOUR;
        require(newTimestamp >= timestamp);
    }
    function addMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp >= timestamp);
    }
    function addSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _seconds;
        require(newTimestamp >= timestamp);
    }

    function subYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year -= _years;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subMonths(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint yearMonth = year * 12 + (month - 1) - _months;
        year = yearMonth / 12;
        month = yearMonth % 12 + 1;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subDays(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _days * SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _hours * SECONDS_PER_HOUR;
        require(newTimestamp <= timestamp);
    }
    function subMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp <= timestamp);
    }
    function subSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _seconds;
        require(newTimestamp <= timestamp);
    }

    function diffYears(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _years) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear,,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear,,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _years = toYear - fromYear;
    }
    function diffMonths(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _months) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear, uint fromMonth,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear, uint toMonth,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _months = toYear * 12 + toMonth - fromYear * 12 - fromMonth;
    }
    function diffDays(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _days) {
        require(fromTimestamp <= toTimestamp);
        _days = (toTimestamp - fromTimestamp) / SECONDS_PER_DAY;
    }
    function diffHours(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _hours) {
        require(fromTimestamp <= toTimestamp);
        _hours = (toTimestamp - fromTimestamp) / SECONDS_PER_HOUR;
    }
    function diffMinutes(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _minutes) {
        require(fromTimestamp <= toTimestamp);
        _minutes = (toTimestamp - fromTimestamp) / SECONDS_PER_MINUTE;
    }
    function diffSeconds(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _seconds) {
        require(fromTimestamp <= toTimestamp);
        _seconds = toTimestamp - fromTimestamp;
    }
}

// File: contracts/libraries/Trigonometry.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

/**
 * @notice Solidity library offering basic trigonometry functions where inputs and outputs are
 * integers. Inputs are specified in radians scaled by 1e18, and similarly outputs are scaled by 1e18.
 *
 * This implementation is based off the Solidity trigonometry library written by Lefteris Karapetsas
 * which can be found here: https://github.com/Sikorkaio/sikorka/blob/e75c91925c914beaedf4841c0336a806f2b5f66d/contracts/trigonometry.sol
 *
 * Compared to Lefteris' implementation, this version makes the following changes:
 *   - Uses a 32 bits instead of 16 bits for improved accuracy
 *   - Updated for Solidity 0.8.x
 *   - Various gas optimizations
 *   - Change inputs/outputs to standard trig format (scaled by 1e18) instead of requiring the
 *     integer format used by the algorithm
 *
 * Lefertis' implementation is based off Dave Dribin's trigint C library
 *     http://www.dribin.org/dave/trigint/
 *
 * Which in turn is based from a now deleted article which can be found in the Wayback Machine:
 *     http://web.archive.org/web/20120301144605/http://www.dattalo.com/technical/software/pic/picsine.html
 */
library Trigonometry {
  // Table index into the trigonometric table
  uint256 constant INDEX_WIDTH        = 8;
  // Interpolation between successive entries in the table
  uint256 constant INTERP_WIDTH       = 16;
  uint256 constant INDEX_OFFSET       = 28 - INDEX_WIDTH;
  uint256 constant INTERP_OFFSET      = INDEX_OFFSET - INTERP_WIDTH;
  uint32  constant ANGLES_IN_CYCLE    = 1073741824;
  uint32  constant QUADRANT_HIGH_MASK = 536870912;
  uint32  constant QUADRANT_LOW_MASK  = 268435456;
  uint256 constant SINE_TABLE_SIZE    = 256;

  // Pi as an 18 decimal value, which is plenty of accuracy: "For JPL's highest accuracy calculations, which are for
  // interplanetary navigation, we use 3.141592653589793: https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/
  uint256 constant PI          = 3141592653589793238;
  uint256 constant TWO_PI      = 2 * PI;
  uint256 constant PI_OVER_TWO = PI / 2;

  // The constant sine lookup table was generated by generate_trigonometry.py. We must use a constant
  // bytes array because constant arrays are not supported in Solidity. Each entry in the lookup
  // table is 4 bytes. Since we're using 32-bit parameters for the lookup table, we get a table size
  // of 2^(32/4) + 1 = 257, where the first and last entries are equivalent (hence the table size of
  // 256 defined above)
  uint8   constant entry_bytes = 4; // each entry in the lookup table is 4 bytes
  uint256 constant entry_mask  = ((1 << 8*entry_bytes) - 1); // mask used to cast bytes32 -> lookup table entry
  bytes   constant sin_table   = hex"00_00_00_00_00_c9_0f_88_01_92_1d_20_02_5b_26_d7_03_24_2a_bf_03_ed_26_e6_04_b6_19_5d_05_7f_00_35_06_47_d9_7c_07_10_a3_45_07_d9_5b_9e_08_a2_00_9a_09_6a_90_49_0a_33_08_bc_0a_fb_68_05_0b_c3_ac_35_0c_8b_d3_5e_0d_53_db_92_0e_1b_c2_e4_0e_e3_87_66_0f_ab_27_2b_10_72_a0_48_11_39_f0_cf_12_01_16_d5_12_c8_10_6e_13_8e_db_b1_14_55_76_b1_15_1b_df_85_15_e2_14_44_16_a8_13_05_17_6d_d9_de_18_33_66_e8_18_f8_b8_3c_19_bd_cb_f3_1a_82_a0_25_1b_47_32_ef_1c_0b_82_6a_1c_cf_8c_b3_1d_93_4f_e5_1e_56_ca_1e_1f_19_f9_7b_1f_dc_dc_1b_20_9f_70_1c_21_61_b3_9f_22_23_a4_c5_22_e5_41_af_23_a6_88_7e_24_67_77_57_25_28_0c_5d_25_e8_45_b6_26_a8_21_85_27_67_9d_f4_28_26_b9_28_28_e5_71_4a_29_a3_c4_85_2a_61_b1_01_2b_1f_34_eb_2b_dc_4e_6f_2c_98_fb_ba_2d_55_3a_fb_2e_11_0a_62_2e_cc_68_1e_2f_87_52_62_30_41_c7_60_30_fb_c5_4d_31_b5_4a_5d_32_6e_54_c7_33_26_e2_c2_33_de_f2_87_34_96_82_4f_35_4d_90_56_36_04_1a_d9_36_ba_20_13_37_6f_9e_46_38_24_93_b0_38_d8_fe_93_39_8c_dd_32_3a_40_2d_d1_3a_f2_ee_b7_3b_a5_1e_29_3c_56_ba_70_3d_07_c1_d5_3d_b8_32_a5_3e_68_0b_2c_3f_17_49_b7_3f_c5_ec_97_40_73_f2_1d_41_21_58_9a_41_ce_1e_64_42_7a_41_d0_43_25_c1_35_43_d0_9a_ec_44_7a_cd_50_45_24_56_bc_45_cd_35_8f_46_75_68_27_47_1c_ec_e6_47_c3_c2_2e_48_69_e6_64_49_0f_57_ee_49_b4_15_33_4a_58_1c_9d_4a_fb_6c_97_4b_9e_03_8f_4c_3f_df_f3_4c_e1_00_34_4d_81_62_c3_4e_21_06_17_4e_bf_e8_a4_4f_5e_08_e2_4f_fb_65_4c_50_97_fc_5e_51_33_cc_94_51_ce_d4_6e_52_69_12_6e_53_02_85_17_53_9b_2a_ef_54_33_02_7d_54_ca_0a_4a_55_60_40_e2_55_f5_a4_d2_56_8a_34_a9_57_1d_ee_f9_57_b0_d2_55_58_42_dd_54_58_d4_0e_8c_59_64_64_97_59_f3_de_12_5a_82_79_99_5b_10_35_ce_5b_9d_11_53_5c_29_0a_cc_5c_b4_20_df_5d_3e_52_36_5d_c7_9d_7b_5e_50_01_5d_5e_d7_7c_89_5f_5e_0d_b2_5f_e3_b3_8d_60_68_6c_ce_60_ec_38_2f_61_6f_14_6b_61_f1_00_3e_62_71_fa_68_62_f2_01_ac_63_71_14_cc_63_ef_32_8f_64_6c_59_bf_64_e8_89_25_65_63_bf_91_65_dd_fb_d2_66_57_3c_bb_66_cf_81_1f_67_46_c7_d7_67_bd_0f_bc_68_32_57_aa_68_a6_9e_80_69_19_e3_1f_69_8c_24_6b_69_fd_61_4a_6a_6d_98_a3_6a_dc_c9_64_6b_4a_f2_78_6b_b8_12_d0_6c_24_29_5f_6c_8f_35_1b_6c_f9_34_fb_6d_62_27_f9_6d_ca_0d_14_6e_30_e3_49_6e_96_a9_9c_6e_fb_5f_11_6f_5f_02_b1_6f_c1_93_84_70_23_10_99_70_83_78_fe_70_e2_cb_c5_71_41_08_04_71_9e_2c_d1_71_fa_39_48_72_55_2c_84_72_af_05_a6_73_07_c3_cf_73_5f_66_25_73_b5_eb_d0_74_0b_53_fa_74_5f_9d_d0_74_b2_c8_83_75_04_d3_44_75_55_bd_4b_75_a5_85_ce_75_f4_2c_0a_76_41_af_3c_76_8e_0e_a5_76_d9_49_88_77_23_5f_2c_77_6c_4e_da_77_b4_17_df_77_fa_b9_88_78_40_33_28_78_84_84_13_78_c7_ab_a1_79_09_a9_2c_79_4a_7c_11_79_8a_23_b0_79_c8_9f_6d_7a_05_ee_ac_7a_42_10_d8_7a_7d_05_5a_7a_b6_cb_a3_7a_ef_63_23_7b_26_cb_4e_7b_5d_03_9d_7b_92_0b_88_7b_c5_e2_8f_7b_f8_88_2f_7c_29_fb_ed_7c_5a_3d_4f_7c_89_4b_dd_7c_b7_27_23_7c_e3_ce_b1_7d_0f_42_17_7d_39_80_eb_7d_62_8a_c5_7d_8a_5f_3f_7d_b0_fd_f7_7d_d6_66_8e_7d_fa_98_a7_7e_1d_93_e9_7e_3f_57_fe_7e_5f_e4_92_7e_7f_39_56_7e_9d_55_fb_7e_ba_3a_38_7e_d5_e5_c5_7e_f0_58_5f_7f_09_91_c3_7f_21_91_b3_7f_38_57_f5_7f_4d_e4_50_7f_62_36_8e_7f_75_4e_7f_7f_87_2b_f2_7f_97_ce_bc_7f_a7_36_b3_7f_b5_63_b2_7f_c2_55_95_7f_ce_0c_3d_7f_d8_87_8d_7f_e1_c7_6a_7f_e9_cb_bf_7f_f0_94_77_7f_f6_21_81_7f_fa_72_d0_7f_fd_88_59_7f_ff_62_15_7f_ff_ff_ff";

  /**
   * @notice Return the sine of a value, specified in radians scaled by 1e18
   * @dev This algorithm for converting sine only uses integer values, and it works by dividing the
   * circle into 30 bit angles, i.e. there are 1,073,741,824 (2^30) angle units, instead of the
   * standard 360 degrees (2pi radians). From there, we get an output in range -2,147,483,647 to
   * 2,147,483,647, (which is the max value of an int32) which is then converted back to the standard
   * range of -1 to 1, again scaled by 1e18
   * @param _angle Angle to convert
   * @return Result scaled by 1e18
   */
  function sin(uint256 _angle) internal pure returns (int256) {
    unchecked {
      // Convert angle from from arbitrary radian value (range of 0 to 2pi) to the algorithm's range
      // of 0 to 1,073,741,824
      _angle = ANGLES_IN_CYCLE * (_angle % TWO_PI) / TWO_PI;

      // Apply a mask on an integer to extract a certain number of bits, where angle is the integer
      // whose bits we want to get, the width is the width of the bits (in bits) we want to extract,
      // and the offset is the offset of the bits (in bits) we want to extract. The result is an
      // integer containing _width bits of _value starting at the offset bit
      uint256 interp = (_angle >> INTERP_OFFSET) & ((1 << INTERP_WIDTH) - 1);
      uint256 index  = (_angle >> INDEX_OFFSET)  & ((1 << INDEX_WIDTH)  - 1);

      // The lookup table only contains data for one quadrant (since sin is symmetric around both
      // axes), so here we figure out which quadrant we're in, then we lookup the values in the
      // table then modify values accordingly
      bool is_odd_quadrant      = (_angle & QUADRANT_LOW_MASK)  == 0;
      bool is_negative_quadrant = (_angle & QUADRANT_HIGH_MASK) != 0;

      if (!is_odd_quadrant) {
        index = SINE_TABLE_SIZE - 1 - index;
      }

      bytes memory table = sin_table;
      // We are looking for two consecutive indices in our lookup table
      // Since EVM is left aligned, to read n bytes of data from idx i, we must read from `i * data_len` + `n`
      // therefore, to read two entries of size entry_bytes `index * entry_bytes` + `entry_bytes * 2`
      uint256 offset1_2 = (index + 2) * entry_bytes;

      // This following snippet will function for any entry_bytes <= 15
      uint256 x1_2; assembly {
        // mload will grab one word worth of bytes (32), as that is the minimum size in EVM
        x1_2 := mload(add(table, offset1_2))
      }

      // We now read the last two numbers of size entry_bytes from x1_2
      // in example: entry_bytes = 4; x1_2 = 0x00...12345678abcdefgh
      // therefore: entry_mask = 0xFFFFFFFF

      // 0x00...12345678abcdefgh >> 8*4 = 0x00...12345678
      // 0x00...12345678 & 0xFFFFFFFF = 0x12345678
      uint256 x1 = x1_2 >> 8*entry_bytes & entry_mask;
      // 0x00...12345678abcdefgh & 0xFFFFFFFF = 0xabcdefgh
      uint256 x2 = x1_2 & entry_mask;

      // Approximate angle by interpolating in the table, accounting for the quadrant
      uint256 approximation = ((x2 - x1) * interp) >> INTERP_WIDTH;
      int256 sine = is_odd_quadrant ? int256(x1) + int256(approximation) : int256(x2) - int256(approximation);
      if (is_negative_quadrant) {
        sine *= -1;
      }

      // Bring result from the range of -2,147,483,647 through 2,147,483,647 to -1e18 through 1e18.
      // This can never overflow because sine is bounded by the above values
      return sine * 1e18 / 2_147_483_647;
    }
  }

  /**
   * @notice Return the cosine of a value, specified in radians scaled by 1e18
   * @dev This is identical to the sin() method, and just computes the value by delegating to the
   * sin() method using the identity cos(x) = sin(x + pi/2)
   * @dev Overflow when `angle + PI_OVER_TWO > type(uint256).max` is ok, results are still accurate
   * @param _angle Angle to convert
   * @return Result scaled by 1e18
   */
  function cos(uint256 _angle) internal pure returns (int256) {
    unchecked {
      return sin(_angle + PI_OVER_TWO);
    }
  }
}
// File: @prb/math/contracts/PRBMathSD59x18.sol



// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;

import "./PRBMath.sol";

/// @title PRBMathSD59x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with int256 numbers considered to have 18
/// trailing decimals. We call this number representation signed 59.18-decimal fixed-point, since the numbers can have
/// a sign and there can be up to 59 digits in the integer part and up to 18 decimals in the fractional part. The numbers
/// are bound by the minimum and the maximum values permitted by the Solidity type int256.
library PRBMathSD59x18 {
    /// @dev log2(e) as a signed 59.18-decimal fixed-point number.
    int256 internal constant LOG2_E = 1_442695040888963407;

    /// @dev Half the SCALE number.
    int256 internal constant HALF_SCALE = 5e17;

    /// @dev The maximum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_792003956564819967;

    /// @dev The maximum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_WHOLE_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev The minimum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_792003956564819968;

    /// @dev The minimum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_WHOLE_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev How many trailing decimals can be represented.
    int256 internal constant SCALE = 1e18;

    /// INTERNAL FUNCTIONS ///

    /// @notice Calculate the absolute value of x.
    ///
    /// @dev Requirements:
    /// - x must be greater than MIN_SD59x18.
    ///
    /// @param x The number to calculate the absolute value for.
    /// @param result The absolute value of x.
    function abs(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x == MIN_SD59x18) {
                revert PRBMathSD59x18__AbsInputTooSmall();
            }
            result = x < 0 ? -x : x;
        }
    }

    /// @notice Calculates the arithmetic average of x and y, rounding down.
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The arithmetic average as a signed 59.18-decimal fixed-point number.
    function avg(int256 x, int256 y) internal pure returns (int256 result) {
        // The operations can never overflow.
        unchecked {
            int256 sum = (x >> 1) + (y >> 1);
            if (sum < 0) {
                // If at least one of x and y is odd, we add 1 to the result. This is because shifting negative numbers to the
                // right rounds down to infinity.
                assembly {
                    result := add(sum, and(or(x, y), 1))
                }
            } else {
                // If both x and y are odd, we add 1 to the result. This is because if both numbers are odd, the 0.5
                // remainder gets truncated twice.
                result = sum + (x & y & 1);
            }
        }
    }

    /// @notice Yields the least greatest signed 59.18 decimal fixed-point number greater than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be less than or equal to MAX_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to ceil.
    /// @param result The least integer greater than or equal to x, as a signed 58.18-decimal fixed-point number.
    function ceil(int256 x) internal pure returns (int256 result) {
        if (x > MAX_WHOLE_SD59x18) {
            revert PRBMathSD59x18__CeilOverflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x > 0) {
                    result += SCALE;
                }
            }
        }
    }

    /// @notice Divides two signed 59.18-decimal fixed-point numbers, returning a new signed 59.18-decimal fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDiv".
    /// - None of the inputs can be MIN_SD59x18.
    /// - The denominator cannot be zero.
    /// - The result must fit within int256.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDiv".
    ///
    /// @param x The numerator as a signed 59.18-decimal fixed-point number.
    /// @param y The denominator as a signed 59.18-decimal fixed-point number.
    /// @param result The quotient as a signed 59.18-decimal fixed-point number.
    function div(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__DivInputTooSmall();
        }

        // Get hold of the absolute values of x and y.
        uint256 ax;
        uint256 ay;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
        }

        // Compute the absolute value of (x*SCALE)÷y. The result must fit within int256.
        uint256 rAbs = PRBMath.mulDiv(ax, uint256(SCALE), ay);
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__DivOverflow(rAbs);
        }

        // Get the signs of x and y.
        uint256 sx;
        uint256 sy;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
        }

        // XOR over sx and sy. This is basically checking whether the inputs have the same sign. If yes, the result
        // should be positive. Otherwise, it should be negative.
        result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns Euler's number as a signed 59.18-decimal fixed-point number.
    /// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
    function e() internal pure returns (int256 result) {
        result = 2_718281828459045235;
    }

    /// @notice Calculates the natural exponent of x.
    ///
    /// @dev Based on the insight that e^x = 2^(x * log2(e)).
    ///
    /// Requirements:
    /// - All from "log2".
    /// - x must be less than 133.084258667509499441.
    ///
    /// Caveats:
    /// - All from "exp2".
    /// - For any x less than -41.446531673892822322, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp(int256 x) internal pure returns (int256 result) {
        // Without this check, the value passed to "exp2" would be less than -59.794705707972522261.
        if (x < -41_446531673892822322) {
            return 0;
        }

        // Without this check, the value passed to "exp2" would be greater than 192.
        if (x >= 133_084258667509499441) {
            revert PRBMathSD59x18__ExpInputTooBig(x);
        }

        // Do the fixed-point multiplication inline to save gas.
        unchecked {
            int256 doubleScaleProduct = x * LOG2_E;
            result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
        }
    }

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    ///
    /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
    ///
    /// Requirements:
    /// - x must be 192 or less.
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - For any x less than -59.794705707972522261, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp2(int256 x) internal pure returns (int256 result) {
        // This works because 2^(-x) = 1/2^x.
        if (x < 0) {
            // 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
            if (x < -59_794705707972522261) {
                return 0;
            }

            // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
            unchecked {
                result = 1e36 / exp2(-x);
            }
        } else {
            // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
            if (x >= 192e18) {
                revert PRBMathSD59x18__Exp2InputTooBig(x);
            }

            unchecked {
                // Convert x to the 192.64-bit fixed-point format.
                uint256 x192x64 = (uint256(x) << 64) / uint256(SCALE);

                // Safe to convert the result to int256 directly because the maximum input allowed is 192.
                result = int256(PRBMath.exp2(x192x64));
            }
        }
    }

    /// @notice Yields the greatest signed 59.18 decimal fixed-point number less than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be greater than or equal to MIN_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to floor.
    /// @param result The greatest integer less than or equal to x, as a signed 58.18-decimal fixed-point number.
    function floor(int256 x) internal pure returns (int256 result) {
        if (x < MIN_WHOLE_SD59x18) {
            revert PRBMathSD59x18__FloorUnderflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x < 0) {
                    result -= SCALE;
                }
            }
        }
    }

    /// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right
    /// of the radix point for negative numbers.
    /// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
    /// @param x The signed 59.18-decimal fixed-point number to get the fractional part of.
    /// @param result The fractional part of x as a signed 59.18-decimal fixed-point number.
    function frac(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x % SCALE;
        }
    }

    /// @notice Converts a number from basic integer form to signed 59.18-decimal fixed-point representation.
    ///
    /// @dev Requirements:
    /// - x must be greater than or equal to MIN_SD59x18 divided by SCALE.
    /// - x must be less than or equal to MAX_SD59x18 divided by SCALE.
    ///
    /// @param x The basic integer to convert.
    /// @param result The same number in signed 59.18-decimal fixed-point representation.
    function fromInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < MIN_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntUnderflow(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntOverflow(x);
            }
            result = x * SCALE;
        }
    }

    /// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
    ///
    /// @dev Requirements:
    /// - x * y must fit within MAX_SD59x18, lest it overflows.
    /// - x * y cannot be negative.
    ///
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function gm(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            return 0;
        }

        unchecked {
            // Checking for overflow this way is faster than letting Solidity do it.
            int256 xy = x * y;
            if (xy / x != y) {
                revert PRBMathSD59x18__GmOverflow(x, y);
            }

            // The product cannot be negative.
            if (xy < 0) {
                revert PRBMathSD59x18__GmNegativeProduct(x, y);
            }

            // We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
            // during multiplication. See the comments within the "sqrt" function.
            result = int256(PRBMath.sqrt(uint256(xy)));
        }
    }

    /// @notice Calculates 1 / x, rounding toward zero.
    ///
    /// @dev Requirements:
    /// - x cannot be zero.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the inverse.
    /// @return result The inverse as a signed 59.18-decimal fixed-point number.
    function inv(int256 x) internal pure returns (int256 result) {
        unchecked {
            // 1e36 is SCALE * SCALE.
            result = 1e36 / x;
        }
    }

    /// @notice Calculates the natural logarithm of x.
    ///
    /// @dev Based on the insight that ln(x) = log2(x) / log2(e).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    /// - This doesn't return exactly 1 for 2718281828459045235, for that we would need more fine-grained precision.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the natural logarithm.
    /// @return result The natural logarithm as a signed 59.18-decimal fixed-point number.
    function ln(int256 x) internal pure returns (int256 result) {
        // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
        // can return is 195205294292027477728.
        unchecked {
            result = (log2(x) * SCALE) / LOG2_E;
        }
    }

    /// @notice Calculates the common logarithm of x.
    ///
    /// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
    /// logarithm based on the insight that log10(x) = log2(x) / log2(10).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the common logarithm.
    /// @return result The common logarithm as a signed 59.18-decimal fixed-point number.
    function log10(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }

        // Note that the "mul" in this block is the assembly mul operation, not the "mul" function defined in this contract.
        // prettier-ignore
        assembly {
            switch x
            case 1 { result := mul(SCALE, sub(0, 18)) }
            case 10 { result := mul(SCALE, sub(1, 18)) }
            case 100 { result := mul(SCALE, sub(2, 18)) }
            case 1000 { result := mul(SCALE, sub(3, 18)) }
            case 10000 { result := mul(SCALE, sub(4, 18)) }
            case 100000 { result := mul(SCALE, sub(5, 18)) }
            case 1000000 { result := mul(SCALE, sub(6, 18)) }
            case 10000000 { result := mul(SCALE, sub(7, 18)) }
            case 100000000 { result := mul(SCALE, sub(8, 18)) }
            case 1000000000 { result := mul(SCALE, sub(9, 18)) }
            case 10000000000 { result := mul(SCALE, sub(10, 18)) }
            case 100000000000 { result := mul(SCALE, sub(11, 18)) }
            case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
            case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
            case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
            case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
            case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
            case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
            case 1000000000000000000 { result := 0 }
            case 10000000000000000000 { result := SCALE }
            case 100000000000000000000 { result := mul(SCALE, 2) }
            case 1000000000000000000000 { result := mul(SCALE, 3) }
            case 10000000000000000000000 { result := mul(SCALE, 4) }
            case 100000000000000000000000 { result := mul(SCALE, 5) }
            case 1000000000000000000000000 { result := mul(SCALE, 6) }
            case 10000000000000000000000000 { result := mul(SCALE, 7) }
            case 100000000000000000000000000 { result := mul(SCALE, 8) }
            case 1000000000000000000000000000 { result := mul(SCALE, 9) }
            case 10000000000000000000000000000 { result := mul(SCALE, 10) }
            case 100000000000000000000000000000 { result := mul(SCALE, 11) }
            case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
            case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
            case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
            case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
            case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
            case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
            case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
            case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
            case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
            case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
            case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
            case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
            case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
            case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
            case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
            case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
            case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
            case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
            case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
            case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
            case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
            case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
            case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
            case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
            case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
            case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
            case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
            case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
            case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
            case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
            case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
            case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
            case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
            case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
            case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
            case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
            case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
            case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
            case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
            default {
                result := MAX_SD59x18
            }
        }

        if (result == MAX_SD59x18) {
            // Do the fixed-point division inline to save gas. The denominator is log2(10).
            unchecked {
                result = (log2(x) * SCALE) / 3_321928094887362347;
            }
        }
    }

    /// @notice Calculates the binary logarithm of x.
    ///
    /// @dev Based on the iterative approximation algorithm.
    /// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
    ///
    /// Requirements:
    /// - x must be greater than zero.
    ///
    /// Caveats:
    /// - The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as a signed 59.18-decimal fixed-point number.
    function log2(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }
        unchecked {
            // This works because log2(x) = -log2(1/x).
            int256 sign;
            if (x >= SCALE) {
                sign = 1;
            } else {
                sign = -1;
                // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
                assembly {
                    x := div(1000000000000000000000000000000000000, x)
                }
            }

            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = PRBMath.mostSignificantBit(uint256(x / SCALE));

            // The integer part of the logarithm as a signed 59.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255, SCALE is 1e18 and sign is either 1 or -1.
            result = int256(n) * SCALE;

            // This is y = x * 2^(-n).
            int256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == SCALE) {
                return result * sign;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (int256 delta = int256(HALF_SCALE); delta > 0; delta >>= 1) {
                y = (y * y) / SCALE;

                // Is y^2 > 2 and so in the range [2,4)?
                if (y >= 2 * SCALE) {
                    // Add the 2^(-m) factor to the logarithm.
                    result += delta;

                    // Corresponds to z/2 on Wikipedia.
                    y >>= 1;
                }
            }
            result *= sign;
        }
    }

    /// @notice Multiplies two signed 59.18-decimal fixed-point numbers together, returning a new signed 59.18-decimal
    /// fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers and employs constant folding, i.e. the denominator is
    /// always 1e18.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - None of the inputs can be MIN_SD59x18
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    ///
    /// @param x The multiplicand as a signed 59.18-decimal fixed-point number.
    /// @param y The multiplier as a signed 59.18-decimal fixed-point number.
    /// @return result The product as a signed 59.18-decimal fixed-point number.
    function mul(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__MulInputTooSmall();
        }

        unchecked {
            uint256 ax;
            uint256 ay;
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);

            uint256 rAbs = PRBMath.mulDivFixedPoint(ax, ay);
            if (rAbs > uint256(MAX_SD59x18)) {
                revert PRBMathSD59x18__MulOverflow(rAbs);
            }

            uint256 sx;
            uint256 sy;
            assembly {
                sx := sgt(x, sub(0, 1))
                sy := sgt(y, sub(0, 1))
            }
            result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
        }
    }

    /// @notice Returns PI as a signed 59.18-decimal fixed-point number.
    function pi() internal pure returns (int256 result) {
        result = 3_141592653589793238;
    }

    /// @notice Raises x to the power of y.
    ///
    /// @dev Based on the insight that x^y = 2^(log2(x) * y).
    ///
    /// Requirements:
    /// - All from "exp2", "log2" and "mul".
    /// - z cannot be zero.
    ///
    /// Caveats:
    /// - All from "exp2", "log2" and "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x Number to raise to given power y, as a signed 59.18-decimal fixed-point number.
    /// @param y Exponent to raise x to, as a signed 59.18-decimal fixed-point number.
    /// @return result x raised to power y, as a signed 59.18-decimal fixed-point number.
    function pow(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            result = y == 0 ? SCALE : int256(0);
        } else {
            result = exp2(mul(log2(x), y));
        }
    }

    /// @notice Raises x (signed 59.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
    /// famous algorithm "exponentiation by squaring".
    ///
    /// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
    ///
    /// Requirements:
    /// - All from "abs" and "PRBMath.mulDivFixedPoint".
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x The base as a signed 59.18-decimal fixed-point number.
    /// @param y The exponent as an uint256.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function powu(int256 x, uint256 y) internal pure returns (int256 result) {
        uint256 xAbs = uint256(abs(x));

        // Calculate the first iteration of the loop in advance.
        uint256 rAbs = y & 1 > 0 ? xAbs : uint256(SCALE);

        // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
        uint256 yAux = y;
        for (yAux >>= 1; yAux > 0; yAux >>= 1) {
            xAbs = PRBMath.mulDivFixedPoint(xAbs, xAbs);

            // Equivalent to "y % 2 == 1" but faster.
            if (yAux & 1 > 0) {
                rAbs = PRBMath.mulDivFixedPoint(rAbs, xAbs);
            }
        }

        // The result must fit within the 59.18-decimal fixed-point representation.
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__PowuOverflow(rAbs);
        }

        // Is the base negative and the exponent an odd number?
        bool isNegative = x < 0 && y & 1 == 1;
        result = isNegative ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns 1 as a signed 59.18-decimal fixed-point number.
    function scale() internal pure returns (int256 result) {
        result = SCALE;
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Requirements:
    /// - x cannot be negative.
    /// - x must be less than MAX_SD59x18 / SCALE.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the square root.
    /// @return result The result as a signed 59.18-decimal fixed-point .
    function sqrt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < 0) {
                revert PRBMathSD59x18__SqrtNegativeInput(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__SqrtOverflow(x);
            }
            // Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two signed
            // 59.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
            result = int256(PRBMath.sqrt(uint256(x * SCALE)));
        }
    }

    /// @notice Converts a signed 59.18-decimal fixed-point number to basic integer form, rounding down in the process.
    /// @param x The signed 59.18-decimal fixed-point number to convert.
    /// @return result The same number in basic integer form.
    function toInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x / SCALE;
        }
    }
}

// File: @openzeppelin/contracts/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// File: contracts/libraries/single-creator/ERC721/ERC721SingleCreatorExtension.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "./ERC721SingleCreatorExtensionBase.sol";

/**
 * @dev Extension that only uses a single creator contract instance
 */
abstract contract ERC721SingleCreatorExtension is ERC721SingleCreatorExtensionBase {

    constructor(address creator) {
        _setCreator(creator);
    }
}
// File: @manifoldxyz/creator-core-solidity/contracts/extensions/ICreatorExtensionTokenURI.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/utils/introspection/IERC165.sol";

/**
 * @dev Implement this if you want your extension to have overloadable URI's
 */
interface ICreatorExtensionTokenURI is IERC165 {

    /**
     * Get the uri for a given creator/tokenId
     */
    function tokenURI(address creator, uint256 tokenId) external view returns (string memory);
}

// File: @manifoldxyz/creator-core-solidity/contracts/extensions/CreatorExtension.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/utils/introspection/ERC165.sol";

/**
 * @dev Base creator extension variables
 */
abstract contract CreatorExtension is ERC165 {

    /**
     * @dev Legacy extension interface identifiers
     *
     * {IERC165-supportsInterface} needs to return 'true' for this interface
     * in order backwards compatible with older creator contracts
     */
    bytes4 constant internal LEGACY_EXTENSION_INTERFACE = 0x7005caad;

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165) returns (bool) {
        return interfaceId == LEGACY_EXTENSION_INTERFACE
            || super.supportsInterface(interfaceId);
    }
    
}
// File: @manifoldxyz/creator-core-solidity/contracts/core/IERC721CreatorCore.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "./ICreatorCore.sol";

/**
 * @dev Core ERC721 creator interface
 */
interface IERC721CreatorCore is ICreatorCore {

    /**
     * @dev mint a token with no extension. Can only be called by an admin.
     * Returns tokenId minted
     */
    function mintBase(address to) external returns (uint256);

    /**
     * @dev mint a token with no extension. Can only be called by an admin.
     * Returns tokenId minted
     */
    function mintBase(address to, string calldata uri) external returns (uint256);

    /**
     * @dev batch mint a token with no extension. Can only be called by an admin.
     * Returns tokenId minted
     */
    function mintBaseBatch(address to, uint16 count) external returns (uint256[] memory);

    /**
     * @dev batch mint a token with no extension. Can only be called by an admin.
     * Returns tokenId minted
     */
    function mintBaseBatch(address to, string[] calldata uris) external returns (uint256[] memory);

    /**
     * @dev mint a token. Can only be called by a registered extension.
     * Returns tokenId minted
     */
    function mintExtension(address to) external returns (uint256);

    /**
     * @dev mint a token. Can only be called by a registered extension.
     * Returns tokenId minted
     */
    function mintExtension(address to, string calldata uri) external returns (uint256);

    /**
     * @dev batch mint a token. Can only be called by a registered extension.
     * Returns tokenIds minted
     */
    function mintExtensionBatch(address to, uint16 count) external returns (uint256[] memory);

    /**
     * @dev batch mint a token. Can only be called by a registered extension.
     * Returns tokenId minted
     */
    function mintExtensionBatch(address to, string[] calldata uris) external returns (uint256[] memory);

    /**
     * @dev burn a token. Can only be called by token owner or approved address.
     * On burn, calls back to the registered extension's onBurn method
     */
    function burn(uint256 tokenId) external;

}
// File: @openzeppelin/contracts/utils/Strings.sol



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

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @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] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (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 Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing 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: @prb/math/contracts/PRBMath.sol



// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);

/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);

/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();

/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();

/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);

/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);

/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);

/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);

/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);

/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);

/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);

/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);

/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);

/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);

/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);

/// @notice Emitted when the calculating the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);

/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);

/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
library PRBMath {
    /// STRUCTS ///

    struct SD59x18 {
        int256 value;
    }

    struct UD60x18 {
        uint256 value;
    }

    /// STORAGE ///

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @dev Largest power of two divisor of SCALE.
    uint256 internal constant SCALE_LPOTD = 262144;

    /// @dev SCALE inverted mod 2^256.
    uint256 internal constant SCALE_INVERSE =
        78156646155174841979727994598816262306175212592076161876661_508869554232690281;

    /// FUNCTIONS ///

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    /// @dev Has to use 192.64-bit fixed-point numbers.
    /// See https://ethereum.stackexchange.com/a/96594/24693.
    /// @param x The exponent as an unsigned 192.64-bit fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp2(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            // Start from 0.5 in the 192.64-bit fixed-point format.
            result = 0x800000000000000000000000000000000000000000000000;

            // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
            // because the initial result is 2^191 and all magic factors are less than 2^65.
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }

            // We're doing two things at the same time:
            //
            //   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
            //      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
            //      rather than 192.
            //   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
            //
            // This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
            result *= SCALE;
            result >>= (191 - (x >> 64));
        }
    }

    /// @notice Finds the zero-based index of the first one in the binary representation of x.
    /// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
    /// @param x The uint256 number for which to find the index of the most significant bit.
    /// @return msb The index of the most significant bit as an uint256.
    function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
        if (x >= 2**128) {
            x >>= 128;
            msb += 128;
        }
        if (x >= 2**64) {
            x >>= 64;
            msb += 64;
        }
        if (x >= 2**32) {
            x >>= 32;
            msb += 32;
        }
        if (x >= 2**16) {
            x >>= 16;
            msb += 16;
        }
        if (x >= 2**8) {
            x >>= 8;
            msb += 8;
        }
        if (x >= 2**4) {
            x >>= 4;
            msb += 4;
        }
        if (x >= 2**2) {
            x >>= 2;
            msb += 2;
        }
        if (x >= 2**1) {
            // No need to shift x any more.
            msb += 1;
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The multiplicand as an uint256.
    /// @param y The multiplier as an uint256.
    /// @param denominator The divisor as an uint256.
    /// @return result The result as an uint256.
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 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) {
            unchecked {
                result = prod0 / denominator;
            }
            return result;
        }

        // Make sure the result is less than 2^256. Also prevents denominator == 0.
        if (prod1 >= denominator) {
            revert PRBMath__MulDivOverflow(prod1, denominator);
        }

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

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

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

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

            // 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 floor(x*y÷1e18) with full precision.
    ///
    /// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
    /// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
    /// being rounded to 1e-18.  See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
    ///
    /// Requirements:
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    /// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
    ///     1. x * y = type(uint256).max * SCALE
    ///     2. (x * y) % SCALE >= SCALE / 2
    ///
    /// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
        uint256 prod0;
        uint256 prod1;
        assembly {
            let mm := mulmod(x, y, not(0))
            prod0 := mul(x, y)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        if (prod1 >= SCALE) {
            revert PRBMath__MulDivFixedPointOverflow(prod1);
        }

        uint256 remainder;
        uint256 roundUpUnit;
        assembly {
            remainder := mulmod(x, y, SCALE)
            roundUpUnit := gt(remainder, 499999999999999999)
        }

        if (prod1 == 0) {
            unchecked {
                result = (prod0 / SCALE) + roundUpUnit;
                return result;
            }
        }

        assembly {
            result := add(
                mul(
                    or(
                        div(sub(prod0, remainder), SCALE_LPOTD),
                        mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
                    ),
                    SCALE_INVERSE
                ),
                roundUpUnit
            )
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - None of the inputs can be type(int256).min.
    /// - The result must fit within int256.
    ///
    /// @param x The multiplicand as an int256.
    /// @param y The multiplier as an int256.
    /// @param denominator The divisor as an int256.
    /// @return result The result as an int256.
    function mulDivSigned(
        int256 x,
        int256 y,
        int256 denominator
    ) internal pure returns (int256 result) {
        if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
            revert PRBMath__MulDivSignedInputTooSmall();
        }

        // Get hold of the absolute values of x, y and the denominator.
        uint256 ax;
        uint256 ay;
        uint256 ad;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
            ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
        }

        // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
        uint256 rAbs = mulDiv(ax, ay, ad);
        if (rAbs > uint256(type(int256).max)) {
            revert PRBMath__MulDivSignedOverflow(rAbs);
        }

        // Get the signs of x, y and the denominator.
        uint256 sx;
        uint256 sy;
        uint256 sd;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
            sd := sgt(denominator, sub(0, 1))
        }

        // XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
        // If yes, the result should be negative.
        result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The uint256 number for which to calculate the square root.
    /// @return result The result as an uint256.
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        // Set the initial guess to the least power of two that is greater than or equal to sqrt(x).
        uint256 xAux = uint256(x);
        result = 1;
        if (xAux >= 0x100000000000000000000000000000000) {
            xAux >>= 128;
            result <<= 64;
        }
        if (xAux >= 0x10000000000000000) {
            xAux >>= 64;
            result <<= 32;
        }
        if (xAux >= 0x100000000) {
            xAux >>= 32;
            result <<= 16;
        }
        if (xAux >= 0x10000) {
            xAux >>= 16;
            result <<= 8;
        }
        if (xAux >= 0x100) {
            xAux >>= 8;
            result <<= 4;
        }
        if (xAux >= 0x10) {
            xAux >>= 4;
            result <<= 2;
        }
        if (xAux >= 0x8) {
            result <<= 1;
        }

        // The operations can never overflow because the result is max 2^127 when it enters this block.
        unchecked {
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1; // Seven iterations should be enough
            uint256 roundedDownResult = x / result;
            return result >= roundedDownResult ? roundedDownResult : result;
        }
    }
}

// File: contracts/libraries/single-creator/ERC721/ERC721SingleCreatorExtensionBase.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/utils/introspection/ERC165Checker.sol";
import "@manifoldxyz/creator-core-solidity/contracts/core/IERC721CreatorCore.sol";

import "../../LegacyInterfaces.sol";
import "../SingleCreatorExtensionBase.sol";

/**
 * @dev Extension that only uses a single creator contract instance
 */
abstract contract ERC721SingleCreatorExtensionBase is SingleCreatorExtensionBase {

    function _setCreator(address creator) internal override {
        require(ERC165Checker.supportsInterface(creator, type(IERC721CreatorCore).interfaceId) ||
                ERC165Checker.supportsInterface(creator, LegacyInterfaces.IERC721CreatorCore_v1), 
                "Creator contract must implement IERC721CreatorCore");
        super._setCreator(creator);
    }
  
}
// File: @openzeppelin/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;
    }
}

// File: @openzeppelin/contracts/utils/introspection/ERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File: @manifoldxyz/creator-core-solidity/contracts/core/ICreatorCore.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

import "@openzeppelin/contracts/utils/introspection/IERC165.sol";

/**
 * @dev Core creator interface
 */
interface ICreatorCore is IERC165 {

    event ExtensionRegistered(address indexed extension, address indexed sender);
    event ExtensionUnregistered(address indexed extension, address indexed sender);
    event ExtensionBlacklisted(address indexed extension, address indexed sender);
    event MintPermissionsUpdated(address indexed extension, address indexed permissions, address indexed sender);
    event RoyaltiesUpdated(uint256 indexed tokenId, address payable[] receivers, uint256[] basisPoints);
    event DefaultRoyaltiesUpdated(address payable[] receivers, uint256[] basisPoints);
    event ExtensionRoyaltiesUpdated(address indexed extension, address payable[] receivers, uint256[] basisPoints);
    event ExtensionApproveTransferUpdated(address indexed extension, bool enabled);

    /**
     * @dev gets address of all extensions
     */
    function getExtensions() external view returns (address[] memory);

    /**
     * @dev add an extension.  Can only be called by contract owner or admin.
     * extension address must point to a contract implementing ICreatorExtension.
     * Returns True if newly added, False if already added.
     */
    function registerExtension(address extension, string calldata baseURI) external;

    /**
     * @dev add an extension.  Can only be called by contract owner or admin.
     * extension address must point to a contract implementing ICreatorExtension.
     * Returns True if newly added, False if already added.
     */
    function registerExtension(address extension, string calldata baseURI, bool baseURIIdentical) external;

    /**
     * @dev add an extension.  Can only be called by contract owner or admin.
     * Returns True if removed, False if already removed.
     */
    function unregisterExtension(address extension) external;

    /**
     * @dev blacklist an extension.  Can only be called by contract owner or admin.
     * This function will destroy all ability to reference the metadata of any tokens created
     * by the specified extension. It will also unregister the extension if needed.
     * Returns True if removed, False if already removed.
     */
    function blacklistExtension(address extension) external;

    /**
     * @dev set the baseTokenURI of an extension.  Can only be called by extension.
     */
    function setBaseTokenURIExtension(string calldata uri) external;

    /**
     * @dev set the baseTokenURI of an extension.  Can only be called by extension.
     * For tokens with no uri configured, tokenURI will return "uri+tokenId"
     */
    function setBaseTokenURIExtension(string calldata uri, bool identical) external;

    /**
     * @dev set the common prefix of an extension.  Can only be called by extension.
     * If configured, and a token has a uri set, tokenURI will return "prefixURI+tokenURI"
     * Useful if you want to use ipfs/arweave
     */
    function setTokenURIPrefixExtension(string calldata prefix) external;

    /**
     * @dev set the tokenURI of a token extension.  Can only be called by extension that minted token.
     */
    function setTokenURIExtension(uint256 tokenId, string calldata uri) external;

    /**
     * @dev set the tokenURI of a token extension for multiple tokens.  Can only be called by extension that minted token.
     */
    function setTokenURIExtension(uint256[] memory tokenId, string[] calldata uri) external;

    /**
     * @dev set the baseTokenURI for tokens with no extension.  Can only be called by owner/admin.
     * For tokens with no uri configured, tokenURI will return "uri+tokenId"
     */
    function setBaseTokenURI(string calldata uri) external;

    /**
     * @dev set the common prefix for tokens with no extension.  Can only be called by owner/admin.
     * If configured, and a token has a uri set, tokenURI will return "prefixURI+tokenURI"
     * Useful if you want to use ipfs/arweave
     */
    function setTokenURIPrefix(string calldata prefix) external;

    /**
     * @dev set the tokenURI of a token with no extension.  Can only be called by owner/admin.
     */
    function setTokenURI(uint256 tokenId, string calldata uri) external;

    /**
     * @dev set the tokenURI of multiple tokens with no extension.  Can only be called by owner/admin.
     */
    function setTokenURI(uint256[] memory tokenIds, string[] calldata uris) external;

    /**
     * @dev set a permissions contract for an extension.  Used to control minting.
     */
    function setMintPermissions(address extension, address permissions) external;

    /**
     * @dev Configure so transfers of tokens created by the caller (must be extension) gets approval
     * from the extension before transferring
     */
    function setApproveTransferExtension(bool enabled) external;

    /**
     * @dev get the extension of a given token
     */
    function tokenExtension(uint256 tokenId) external view returns (address);

    /**
     * @dev Set default royalties
     */
    function setRoyalties(address payable[] calldata receivers, uint256[] calldata basisPoints) external;

    /**
     * @dev Set royalties of a token
     */
    function setRoyalties(uint256 tokenId, address payable[] calldata receivers, uint256[] calldata basisPoints) external;

    /**
     * @dev Set royalties of an extension
     */
    function setRoyaltiesExtension(address extension, address payable[] calldata receivers, uint256[] calldata basisPoints) external;

    /**
     * @dev Get royalites of a token.  Returns list of receivers and basisPoints
     */
    function getRoyalties(uint256 tokenId) external view returns (address payable[] memory, uint256[] memory);
    
    // Royalty support for various other standards
    function getFeeRecipients(uint256 tokenId) external view returns (address payable[] memory);
    function getFeeBps(uint256 tokenId) external view returns (uint[] memory);
    function getFees(uint256 tokenId) external view returns (address payable[] memory, uint256[] memory);
    function royaltyInfo(uint256 tokenId, uint256 value) external view returns (address, uint256);

}

// File: contracts/libraries/single-creator/SingleCreatorExtensionBase.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/// @author: manifold.xyz

/**
 * @dev Extension that only uses a single creator contract instance
 */
abstract contract SingleCreatorExtensionBase {
    address internal _creator;

    /**
     * @dev Override with appropriate interface checks if necessary
     */
    function _setCreator(address creator) internal virtual {
      _creator = creator;
    }

    function creatorContract() public view returns(address) {
        return _creator;
    }
}
// File: contracts/libraries/LegacyInterfaces.sol



// SPDX-License-Identifier: BSD-4-Clause

pragma solidity ^0.8.0;

/// @author: manifold.xyz

/**
 * Library of legacy interface constants
 */
library LegacyInterfaces {

    // LEGACY ERC721CreatorCore interface
    bytes4 internal constant IERC721CreatorCore_v1 = 0x478c8530;

}

// File: @openzeppelin/contracts/utils/introspection/ERC165Checker.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165Checker.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Library used to query support of an interface declared via {IERC165}.
 *
 * Note that these functions return the actual result of the query: they do not
 * `revert` if an interface is not supported. It is up to the caller to decide
 * what to do in these cases.
 */
library ERC165Checker {
    // As per the EIP-165 spec, no interface should ever match 0xffffffff
    bytes4 private constant _INTERFACE_ID_INVALID = 0xffffffff;

    /**
     * @dev Returns true if `account` supports the {IERC165} interface,
     */
    function supportsERC165(address account) internal view returns (bool) {
        // Any contract that implements ERC165 must explicitly indicate support of
        // InterfaceId_ERC165 and explicitly indicate non-support of InterfaceId_Invalid
        return
            _supportsERC165Interface(account, type(IERC165).interfaceId) &&
            !_supportsERC165Interface(account, _INTERFACE_ID_INVALID);
    }

    /**
     * @dev Returns true if `account` supports the interface defined by
     * `interfaceId`. Support for {IERC165} itself is queried automatically.
     *
     * See {IERC165-supportsInterface}.
     */
    function supportsInterface(address account, bytes4 interfaceId) internal view returns (bool) {
        // query support of both ERC165 as per the spec and support of _interfaceId
        return supportsERC165(account) && _supportsERC165Interface(account, interfaceId);
    }

    /**
     * @dev Returns a boolean array where each value corresponds to the
     * interfaces passed in and whether they're supported or not. This allows
     * you to batch check interfaces for a contract where your expectation
     * is that some interfaces may not be supported.
     *
     * See {IERC165-supportsInterface}.
     *
     * _Available since v3.4._
     */
    function getSupportedInterfaces(address account, bytes4[] memory interfaceIds)
        internal
        view
        returns (bool[] memory)
    {
        // an array of booleans corresponding to interfaceIds and whether they're supported or not
        bool[] memory interfaceIdsSupported = new bool[](interfaceIds.length);

        // query support of ERC165 itself
        if (supportsERC165(account)) {
            // query support of each interface in interfaceIds
            for (uint256 i = 0; i < interfaceIds.length; i++) {
                interfaceIdsSupported[i] = _supportsERC165Interface(account, interfaceIds[i]);
            }
        }

        return interfaceIdsSupported;
    }

    /**
     * @dev Returns true if `account` supports all the interfaces defined in
     * `interfaceIds`. Support for {IERC165} itself is queried automatically.
     *
     * Batch-querying can lead to gas savings by skipping repeated checks for
     * {IERC165} support.
     *
     * See {IERC165-supportsInterface}.
     */
    function supportsAllInterfaces(address account, bytes4[] memory interfaceIds) internal view returns (bool) {
        // query support of ERC165 itself
        if (!supportsERC165(account)) {
            return false;
        }

        // query support of each interface in _interfaceIds
        for (uint256 i = 0; i < interfaceIds.length; i++) {
            if (!_supportsERC165Interface(account, interfaceIds[i])) {
                return false;
            }
        }

        // all interfaces supported
        return true;
    }

    /**
     * @notice Query if a contract implements an interface, does not check ERC165 support
     * @param account The address of the contract to query for support of an interface
     * @param interfaceId The interface identifier, as specified in ERC-165
     * @return true if the contract at account indicates support of the interface with
     * identifier interfaceId, false otherwise
     * @dev Assumes that account contains a contract that supports ERC165, otherwise
     * the behavior of this method is undefined. This precondition can be checked
     * with {supportsERC165}.
     * Interface identification is specified in ERC-165.
     */
    function _supportsERC165Interface(address account, bytes4 interfaceId) private view returns (bool) {
        bytes memory encodedParams = abi.encodeWithSelector(IERC165.supportsInterface.selector, interfaceId);
        (bool success, bytes memory result) = account.staticcall{gas: 30000}(encodedParams);
        if (result.length < 32) return false;
        return success && abi.decode(result, (bool));
    }
}