// File: LostPetsRenderer.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.14;

import {Strings} from "@openzeppelin/contracts/utils/Strings.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import {DynamicBuffer} from "@divergencetech/ethier/contracts/utils/DynamicBuffer.sol";
import {Base64} from "./Base64.sol";

import {ILostPetsStore} from "./interfaces/ILostPetsStore.sol";
import {ILostPetsRenderer} from "./interfaces/ILostPetsRenderer.sol";
import {IExquisiteGraphics} from "./interfaces/IExquisiteGraphics.sol";

contract LostPetsRenderer is ILostPetsRenderer, Ownable {
    using Strings for uint256;
    using DynamicBuffer for bytes;

    ILostPetsStore public dataStore;
    IExquisiteGraphics public xqstgfx;

    constructor(
        address inLostPetsStore,
        address inxqstgfx
    ) {
        dataStore = ILostPetsStore(inLostPetsStore);
        xqstgfx = IExquisiteGraphics(inxqstgfx);
    }

    function setXqstGfx(IExquisiteGraphics newXqstgfx) external onlyOwner
    {
        xqstgfx = newXqstgfx;
    }
    
    function setDataStore(ILostPetsStore newDataStore) external onlyOwner
    {
        dataStore = newDataStore;
    }

    function SVGToString(bytes memory data) public view returns (string memory) {
        return string(SVGToBytes(data));
    }

    function SVGToBytes(bytes memory data) public view returns (bytes memory) {
        string memory rects = xqstgfx.drawPixelsUnsafe(data);
        bytes memory svg = DynamicBuffer.allocate(2**19);

        svg.appendSafe(
            abi.encodePacked(
                '<svg xmlns="http://www.w3.org/2000/svg" shape-rendering="crispEdges" width="100%" height="100%" version="1.1" viewBox="0 0 32 32" fill="#fff"><rect width="32" height="32" fill="#fff" /><g>',
                rects,
                "</g></svg>"
            )
        );

        return svg;
    }

    function getLostPetSVG(uint256 id) external view returns (string memory) {
        bytes memory data = dataStore.getRawPetData(id);
        return SVGToString(data);
    }

    function getLostPetBase64SVG(uint256 id) external view returns (string memory) {
        bytes memory data = dataStore.getRawPetData(id);
        if(data.length <= 0) {
            return "";
        }

        bytes memory svg = SVGToBytes(data);
        bytes memory svgB64 = DynamicBuffer.allocate(2**19);

        svgB64.appendSafe("data:image/svg+xml;base64,");
        svgB64.appendSafe(bytes(Base64.encode(svg)));

        return string(svgB64);
    }

    function tokenURI(uint256 id) external view returns (string memory) {
        string memory imageString = "";


        bytes memory data = dataStore.getRawPetData(id);
        if(data.length > 0) {
            bytes memory svgB64 = DynamicBuffer.allocate(2**19);
            bytes memory svg = SVGToBytes(data);

            svgB64.appendSafe("data:image/svg+xml;base64,");
            svgB64.appendSafe(bytes(Base64.encode(svg)));
            imageString = string(svgB64);
        }

        bytes memory json = DynamicBuffer.allocate(2**19);
        bytes memory jsonB64 = DynamicBuffer.allocate(2**19);


        json.appendSafe(
            abi.encodePacked(
                '{"symbol":"LOSTPETS","name":"', dataStore.getPetName((uint8)(id)),
                '","description":"200 fully on-chain lost pet portraits. LostPets.NYC"',
                ',"image":"', imageString, '"',
                ',"attributes":[{"trait_type":"Pet Type","value":"', dataStore.getPetType((uint8)(id)), '"}',
                ',{"trait_type":"Breed","value":"', dataStore.getPetBreed((uint8)(id)), '"}',
                ',{"trait_type":"Neighborhood","value":"', dataStore.getPetHood((uint8)(id)), '"}'
            )
        );

        json.appendSafe(
            abi.encodePacked(
                ',{"trait_type":"Status","value":"', dataStore.getPetState((uint8)(id)), '"}',
                ',{"trait_type":"Borough","value":"', dataStore.getPetBorough((uint8)(id)), '"}',
                ',{"trait_type":"Reward","value":"', dataStore.getPetHasReward((uint8)(id)), '"}',
                ',{"trait_type":"Colors","value":"', dataStore.getPetColors((uint8)(id)), '"}',
                ',{"trait_type":"Palette","value":"', dataStore.getPetPallete((uint8)(id)), '"}]}'
            )
        );

        jsonB64.appendSafe("data:application/json;base64,");
        jsonB64.appendSafe(bytes(Base64.encode(json)));

        return string(jsonB64);
    }
}
// File: interfaces/IExquisiteGraphics.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

interface IExquisiteGraphics {
    struct Header {
        /* HEADER START */
        uint8 version; // 8 bits
        uint16 width; // 8 bits
        uint16 height; // 8 bits
        uint16 numColors; // 16 bits
        uint8 backgroundColorIndex; // 8 bits
        uint16 scale; // 10 bits
        uint8 reserved; // 4 bits
        bool alpha; // 1 bit
        bool hasBackground; // 1 bit
        /* HEADER END */

        /* CALCULATED DATA START */
        uint24 totalPixels; // total pixels in the image
        uint8 bitsPerPixel; // bits per pixel
        uint8 pixelsPerByte; // pixels per byte
        uint16 paletteStart; // number of the byte where the palette starts
        uint16 dataStart; // number of the byte where the data starts
        /* CALCULATED DATA END */
    }

    struct DrawContext {
        bytes data; // the binary data in .xqst format
        Header header; // the header of the data
        string[] palette; // hex color for each color in the image
        uint8[] pixels; // color index (in the palette) for a pixel
    }

    error ExceededMaxPixels();
    error ExceededMaxRows();
    error ExceededMaxColumns();
    error ExceededMaxColors();
    error BackgroundColorIndexOutOfRange();
    error PixelColorIndexOutOfRange();
    error MissingHeader();
    error NotEnoughData();

    /// @notice Draw an SVG from the provided data
    /// @param data Binary data in the .xqst format.
    /// @return string the <svg>
    function draw(bytes memory data) external pure returns (string memory);

    /// @notice Draw an SVG from the provided data. No validation.
    /// @param data Binary data in the .xqst format.
    /// @return string the <svg>
    function drawUnsafe(bytes memory data) external pure returns (string memory);

    /// @notice Draw the <rect> elements of an SVG from the data
    /// @param data Binary data in the .xqst format.
    /// @return string the <rect> elements
    function drawPixels(bytes memory data) external pure returns (string memory);

    /// @notice Draw the <rect> elements of an SVG from the data. No validation
    /// @param data Binary data in the .xqst format.
    /// @return string the <rect> elements
    function drawPixelsUnsafe(bytes memory data) external pure returns (string memory);

    /// @notice validates if the given data is a valid .xqst file
    /// @param data Binary data in the .xqst format.
    /// @return bool true if the data is valid
    function validate(bytes memory data) external pure returns (bool);

    // Check if the header of some data is an XQST Graphics Compatible file
    /// @notice validates the header for some data is a valid .xqst header
    /// @param data Binary data in the .xqst format.
    /// @return bool true if the header is valid
    function validateHeader(bytes memory data) external pure returns (bool);

    /// @notice Decodes the header from a binary .xqst blob
    /// @param data Binary data in the .xqst format.
    /// @return Header the decoded header
    function decodeHeader(bytes memory data) external pure returns (Header memory);

    /// @notice Decodes the palette from a binary .xqst blob
    /// @param data Binary data in the .xqst format.
    /// @return bytes8[] the decoded palette
    function decodePalette(bytes memory data) external pure returns (string[] memory);

    /// @notice Decodes all of the data needed to draw an SVG from the .xqst file
    /// @param data Binary data in the .xqst format.
    /// @return ctx The Draw Context containing all of the decoded data
    function decodeDrawContext(bytes memory data) external pure returns (DrawContext memory ctx);
}
// File: interfaces/ILostPetsRenderer.sol



//SPDX-License-Identifier: MIT
pragma solidity ^0.8.14;

interface ILostPetsRenderer {
    function getLostPetSVG(uint256 id) external view returns (string memory);

    function tokenURI(uint256 id) external view returns (string memory);
}
// File: interfaces/ILostPetsStore.sol



// SPDX-License-Identifier: CC0-1.0
pragma solidity ^0.8.14;

interface ILostPetsStore {
    // function getBaseURI() external view returns (string memory);

    function getPetName(uint256 id) external view returns (string memory);
    function getPetHood(uint256 id) external view returns (string memory);
    function getPetBreed(uint256 id) external view returns (string memory);
    function getPetState(uint8 id) external view returns (string memory);
    function getPetHasReward(uint8 id) external view returns (string memory);
    function getPetPallete(uint8 id) external view returns (string memory);

    function getPetBorough(uint8 id) external view returns (string memory);
    function getPetType(uint8 id) external view returns (string memory);
    function getPetColors(uint8 id) external view returns (string memory);


    function getRawPetData(uint256 id) external view returns (bytes memory);
}
// File: Base64.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

/// [MIT License]
/// @title Base64
/// @notice Provides a function for encoding some bytes in base64
/// @author Brecht Devos <brecht@loopring.org>
library Base64 {
    bytes internal constant TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";

    /// @notice Encodes some bytes to the base64 representation
    function encode(bytes memory data) internal pure returns (string memory) {
        uint256 len = data.length;
        if (len == 0) return "";

        // multiply by 4/3 rounded up
        uint256 encodedLen = 4 * ((len + 2) / 3);

        // Add some extra buffer at the end
        bytes memory result = new bytes(encodedLen + 32);

        bytes memory table = TABLE;

        assembly {
            let tablePtr := add(table, 1)
            let resultPtr := add(result, 32)

            for {
                let i := 0
            } lt(i, len) {

            } {
                i := add(i, 3)
                let input := and(mload(add(data, i)), 0xffffff)

                let out := mload(add(tablePtr, and(shr(18, input), 0x3F)))
                out := shl(8, out)
                out := add(out, and(mload(add(tablePtr, and(shr(12, input), 0x3F))), 0xFF))
                out := shl(8, out)
                out := add(out, and(mload(add(tablePtr, and(shr(6, input), 0x3F))), 0xFF))
                out := shl(8, out)
                out := add(out, and(mload(add(tablePtr, and(input, 0x3F))), 0xFF))
                out := shl(224, out)

                mstore(resultPtr, out)

                resultPtr := add(resultPtr, 4)
            }

            switch mod(len, 3)
            case 1 {
                mstore(sub(resultPtr, 2), shl(240, 0x3d3d))
            }
            case 2 {
                mstore(sub(resultPtr, 1), shl(248, 0x3d))
            }

            mstore(result, encodedLen)
        }

        return string(result);
    }
}
// File: @divergencetech/ethier/contracts/utils/DynamicBuffer.sol



// SPDX-License-Identifier: MIT
// Copyright (c) 2021 the ethier authors (github.com/divergencetech/ethier)

pragma solidity >=0.8.0;

/// @title DynamicBuffer
/// @author David Huber (@cxkoda) and Simon Fremaux (@dievardump). See also
///         https://raw.githubusercontent.com/dievardump/solidity-dynamic-buffer
/// @notice This library is used to allocate a big amount of container memory
//          which will be subsequently filled without needing to reallocate
///         memory.
/// @dev First, allocate memory.
///      Then use `buffer.appendUnchecked(theBytes)` or `appendSafe()` if
///      bounds checking is required.
library DynamicBuffer {
    /// @notice Allocates container space for the DynamicBuffer
    /// @param capacity_ The intended max amount of bytes in the buffer
    /// @return buffer The memory location of the buffer
    /// @dev Allocates `capacity_ + 0x60` bytes of space
    ///      The buffer array starts at the first container data position,
    ///      (i.e. `buffer = container + 0x20`)
    function allocate(uint256 capacity_)
        internal
        pure
        returns (bytes memory buffer)
    {
        assembly {
            // Get next-free memory address
            let container := mload(0x40)

            // Allocate memory by setting a new next-free address
            {
                // Add 2 x 32 bytes in size for the two length fields
                // Add 32 bytes safety space for 32B chunked copy
                let size := add(capacity_, 0x60)
                let newNextFree := add(container, size)
                mstore(0x40, newNextFree)
            }

            // Set the correct container length
            {
                let length := add(capacity_, 0x40)
                mstore(container, length)
            }

            // The buffer starts at idx 1 in the container (0 is length)
            buffer := add(container, 0x20)

            // Init content with length 0
            mstore(buffer, 0)
        }

        return buffer;
    }

    /// @notice Appends data to buffer, and update buffer length
    /// @param buffer the buffer to append the data to
    /// @param data the data to append
    /// @dev Does not perform out-of-bound checks (container capacity)
    ///      for efficiency.
    function appendUnchecked(bytes memory buffer, bytes memory data)
        internal
        pure
    {
        assembly {
            let length := mload(data)
            for {
                data := add(data, 0x20)
                let dataEnd := add(data, length)
                let copyTo := add(buffer, add(mload(buffer), 0x20))
            } lt(data, dataEnd) {
                data := add(data, 0x20)
                copyTo := add(copyTo, 0x20)
            } {
                // Copy 32B chunks from data to buffer.
                // This may read over data array boundaries and copy invalid
                // bytes, which doesn't matter in the end since we will
                // later set the correct buffer length, and have allocated an
                // additional word to avoid buffer overflow.
                mstore(copyTo, mload(data))
            }

            // Update buffer length
            mstore(buffer, add(mload(buffer), length))
        }
    }

    /// @notice Appends data to buffer, and update buffer length
    /// @param buffer the buffer to append the data to
    /// @param data the data to append
    /// @dev Performs out-of-bound checks and calls `appendUnchecked`.
    function appendSafe(bytes memory buffer, bytes memory data) internal pure {
        checkOverflow(buffer, data.length);
        appendUnchecked(buffer, data);
    }

    /// @notice Appends data encoded as Base64 to buffer.
    /// @param fileSafe  Whether to replace '+' with '-' and '/' with '_'.
    /// @param noPadding Whether to strip away the padding.
    /// @dev Encodes `data` using the base64 encoding described in RFC 4648.
    /// See: https://datatracker.ietf.org/doc/html/rfc4648
    /// Author: Modified from Solady (https://github.com/vectorized/solady/blob/main/src/utils/Base64.sol)
    /// Author: Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/Base64.sol)
    /// Author: Modified from (https://github.com/Brechtpd/base64/blob/main/base64.sol) by Brecht Devos.
    function appendSafeBase64(
        bytes memory buffer,
        bytes memory data,
        bool fileSafe,
        bool noPadding
    ) internal pure {
        uint256 dataLength = data.length;

        if (data.length == 0) {
            return;
        }

        uint256 encodedLength;
        uint256 r;
        assembly {
            // For each 3 bytes block, we will have 4 bytes in the base64
            // encoding: `encodedLength = 4 * divCeil(dataLength, 3)`.
            // The `shl(2, ...)` is equivalent to multiplying by 4.
            encodedLength := shl(2, div(add(dataLength, 2), 3))

            r := mod(dataLength, 3)
            if noPadding {
                // if r == 0 => no modification
                // if r == 1 => encodedLength -= 2
                // if r == 2 => encodedLength -= 1
                encodedLength := sub(
                    encodedLength,
                    add(iszero(iszero(r)), eq(r, 1))
                )
            }
        }

        checkOverflow(buffer, encodedLength);

        assembly {
            let nextFree := mload(0x40)

            // Store the table into the scratch space.
            // Offsetted by -1 byte so that the `mload` will load the character.
            // We will rewrite the free memory pointer at `0x40` later with
            // the allocated size.
            mstore(0x1f, "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdef")
            mstore(
                0x3f,
                sub(
                    "ghijklmnopqrstuvwxyz0123456789-_",
                    // The magic constant 0x0230 will translate "-_" + "+/".
                    mul(iszero(fileSafe), 0x0230)
                )
            )

            // Skip the first slot, which stores the length.
            let ptr := add(add(buffer, 0x20), mload(buffer))
            let end := add(data, dataLength)

            // Run over the input, 3 bytes at a time.
            // prettier-ignore
            // solhint-disable-next-line no-empty-blocks
            for {} 1 {} {
                    data := add(data, 3) // Advance 3 bytes.
                    let input := mload(data)

                    // Write 4 bytes. Optimized for fewer stack operations.
                    mstore8(    ptr    , mload(and(shr(18, input), 0x3F)))
                    mstore8(add(ptr, 1), mload(and(shr(12, input), 0x3F)))
                    mstore8(add(ptr, 2), mload(and(shr( 6, input), 0x3F)))
                    mstore8(add(ptr, 3), mload(and(        input , 0x3F)))
                    
                    ptr := add(ptr, 4) // Advance 4 bytes.
                    // prettier-ignore
                    if iszero(lt(data, end)) { break }
                }

            if iszero(noPadding) {
                // Offset `ptr` and pad with '='. We can simply write over the end.
                mstore8(sub(ptr, iszero(iszero(r))), 0x3d) // Pad at `ptr - 1` if `r > 0`.
                mstore8(sub(ptr, shl(1, eq(r, 1))), 0x3d) // Pad at `ptr - 2` if `r == 1`.
            }

            mstore(buffer, add(mload(buffer), encodedLength))
            mstore(0x40, nextFree)
        }
    }

    /// @notice Returns the capacity of a given buffer.
    function capacity(bytes memory buffer) internal pure returns (uint256) {
        uint256 cap;
        assembly {
            cap := sub(mload(sub(buffer, 0x20)), 0x40)
        }
        return cap;
    }

    /// @notice Reverts if the buffer will overflow after appending a given
    /// number of bytes.
    function checkOverflow(bytes memory buffer, uint256 addedLength)
        internal
        pure
    {
        uint256 cap = capacity(buffer);
        uint256 newLength = buffer.length + addedLength;
        if (cap < newLength) {
            revert("DynamicBuffer: Appending out of bounds.");
        }
    }
}

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



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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions 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: @openzeppelin/contracts/utils/Strings.sol



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

pragma solidity ^0.8.0;

import "./math/Math.sol";

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

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

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

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

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

// File: @openzeppelin/contracts/utils/math/Math.sol



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

pragma solidity ^0.8.0;

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

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

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

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

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

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

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

// 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;
    }
}