// File: contracts/TwoFiveSixProject.sol



// SPDX-License-Identifier: MIT

/* 

 222222222222222    555555555555555555         66666666   
2:::::::::::::::22  5::::::::::::::::5        6::::::6    
2::::::222222:::::2 5::::::::::::::::5       6::::::6     
2222222     2:::::2 5:::::555555555555      6::::::6      
            2:::::2 5:::::5                6::::::6       
            2:::::2 5:::::5               6::::::6        
         2222::::2  5:::::5555555555     6::::::6         
    22222::::::22   5:::::::::::::::5   6::::::::66666    
  22::::::::222     555555555555:::::5 6::::::::::::::66  
 2:::::22222                    5:::::56::::::66666:::::6 
2:::::2                         5:::::56:::::6     6:::::6
2:::::2             5555555     5:::::56:::::6     6:::::6
2:::::2       2222225::::::55555::::::56::::::66666::::::6
2::::::2222222:::::2 55:::::::::::::55  66:::::::::::::66 
2::::::::::::::::::2   55:::::::::55      66:::::::::66   
22222222222222222222     555555555          666666666    

Using this contract? A shout out to @Mint256Art is appreciated!
 */

pragma solidity ^0.8.13;

import "./helpers/OwnableUpgradeable.sol";
import "./helpers/ERC721EnumerableUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/Base64Upgradeable.sol";

contract TwoFiveSixProject is ERC721EnumerableUpgradeable, OwnableUpgradeable {
    uint256[180] public memberShipFlags;
    uint256[4] public gmTokenFlags;
    uint256[4] public grailersTokenFlags;
    string public baseURI;

    address public twoFiveSixGenesisAddress;
    address public gmTokenAddress;
    address public grailersAddress;

    uint256 public maxPerTx;
    uint256 public twoFiveSixShare;

    mapping(uint256 => bytes32) public tokenIdToHash;

    struct Project {
        string name;
        address payable artistAddress;
        address payable twoFiveSixFundsAddress;
        address artScriptAddress;
        address royaltyAddress;
        address owner;
        uint256 maxSupply;
        uint256 showCaseAmount;
        uint256 memberPrice;
        uint256 publicPrice;
        uint256 royalty;
        uint256 preSaleTimeStamp;
        uint256 publicTimetamp;
        bool memberOnly;
    }

    Project private project;

    function initProject(
        Project calldata p,
        uint256 _twoFiveSixShare,
        uint256 _maxPerTx,
        address _twoFiveSixGenesisAddress,
        address _gmTokenAddress,
        address _grailersAddress,
        string calldata _baseOfBase
    ) public initializer {
        __ERC721_init(p.name, "256ART");
        __Ownable_init(p.owner);
        project = p;
        maxPerTx = _maxPerTx;
        twoFiveSixShare = _twoFiveSixShare;
        grailersAddress = _grailersAddress;
        gmTokenAddress = _gmTokenAddress;
        twoFiveSixGenesisAddress = _twoFiveSixGenesisAddress;
        baseURI = string(
            abi.encodePacked(
                _baseOfBase,
                _toLower(StringsUpgradeable.toHexString(address(this))),
                "/json_files/"
            )
        );
    }

    function tokenURI(uint256 _tokenId)
        public
        view
        override
        returns (string memory)
    {
        require(_exists(_tokenId), "Token not found");
        return
            string(
                abi.encodePacked(baseURI, StringsUpgradeable.toString(_tokenId))
            );
    }

    function showCaseMint(uint256[] calldata the256ArtIds) public onlyOwner {
        uint256 count = the256ArtIds.length;
        uint256 totalSupply = _owners.length;
        require(totalSupply == 0, "Not first mint");
        require(count == project.showCaseAmount, "Must mint all");
        require(project.showCaseAmount % 2 == 0, "Must be even.");

        IERC721Upgradeable twoFiveSix = IERC721Upgradeable(
            twoFiveSixGenesisAddress
        );

        for (uint256 i; i < count; i++) {
            require(
                twoFiveSix.ownerOf(the256ArtIds[i]) == _msgSender(),
                "Membership not owned"
            );
            uint256 storedValue = getTokenIdForMembershipId(the256ArtIds[i]);
            bool unset = storedValue == 0;

            require(unset, "Membership already used");
        }

        for (uint256 i; i < (project.showCaseAmount / 2); i++) {
            uint256 tokenId = totalSupply + i;
            uint256 tokenIdTwo = totalSupply + i + (project.showCaseAmount / 2);

            bytes32 hashOne = createHash(tokenId, msg.sender);

            tokenIdToHash[tokenId] = hashOne;
            _setTokenIdForMembershipId(the256ArtIds[i], tokenId);

            _mint(project.artistAddress, tokenId);

            bytes32 hashTwo = createHash(tokenIdTwo, msg.sender);
            tokenIdToHash[tokenIdTwo] = hashTwo;

            _setTokenIdForMembershipId(
                the256ArtIds[i + (project.showCaseAmount / 2)],
                tokenIdTwo
            );

            _mint(project.twoFiveSixFundsAddress, tokenIdTwo);
        }
    }

    function memberMint(uint256[] calldata the256ArtIds, address a)
        public
        payable
    {
        uint256 totalSupply = _owners.length;
        uint256 count = the256ArtIds.length;
        require(project.preSaleTimeStamp < block.timestamp, "Sale not active");
        require(count > 0, "Mint at least one");
        require(totalSupply + count < project.maxSupply, "Exceeds max supply.");
        require(count < maxPerTx, "Exceeds max per transaction.");
        require(
            count * project.memberPrice <= msg.value,
            "Invalid funds provided."
        );
        require(msg.sender == tx.origin, "No contract minting");

        IERC721Upgradeable twoFiveSix = IERC721Upgradeable(
            twoFiveSixGenesisAddress
        );

        for (uint256 i; i < count; i++) {
            require(
                twoFiveSix.ownerOf(the256ArtIds[i]) == a,
                "Membership not owned"
            );
            uint256 tokenId = totalSupply + i;

            uint256 storedValue = getTokenIdForMembershipId(the256ArtIds[i]);
            bool unset = (storedValue == 0);

            require(unset, "Membership already used");

            _setTokenIdForMembershipId(the256ArtIds[i], tokenId);

            bytes32 hashOne = createHash(tokenId, msg.sender);
            tokenIdToHash[tokenId] = hashOne;

            _mint(a, tokenId);
        }
    }

    function gmTokenMint(uint256[] calldata gmTokenIds, address a)
        public
        payable
    {
        uint256 totalSupply = _owners.length;
        uint256 count = gmTokenIds.length;
        require(project.preSaleTimeStamp < block.timestamp, "Sale not active");
        require(!project.memberOnly, "Only members can mint.");
        require(count > 0, "Mint at least one");
        require(totalSupply + count < project.maxSupply, "Exceeds max supply.");
        require(count < maxPerTx, "Exceeds max per transaction.");
        require(
            count * project.memberPrice <= msg.value,
            "Invalid funds provided."
        );
        require(msg.sender == tx.origin, "No contract minting");

        IERC721Upgradeable gmToken = IERC721Upgradeable(gmTokenAddress);

        for (uint256 i; i < count; i++) {
            require(gmToken.ownerOf(gmTokenIds[i]) == a, "GmToken not owned");
            uint256 tokenId = totalSupply + i;

            bool isUsed = getGmTokenUsed(gmTokenIds[i]);

            require(!isUsed, "GmToken already used");

            _setGmTokenUsed(gmTokenIds[i]);

            bytes32 hashOne = createHash(tokenId, msg.sender);
            tokenIdToHash[tokenId] = hashOne;

            _mint(a, tokenId);
        }
    }

    function grailersTokenMint(uint256[] calldata grailersTokenIds, address a)
        public
        payable
    {
        uint256 totalSupply = _owners.length;
        uint256 count = grailersTokenIds.length;
        require(project.preSaleTimeStamp < block.timestamp, "Sale not active");
        require(!project.memberOnly, "Only members can mint.");
        require(count > 0, "Mint at least one");
        require(totalSupply + count < project.maxSupply, "Exceeds max supply.");
        require(count < maxPerTx, "Exceeds max per transaction.");
        require(
            count * project.memberPrice <= msg.value,
            "Invalid funds provided."
        );
        require(msg.sender == tx.origin, "No contract minting");

        IERC721Upgradeable grailersToken = IERC721Upgradeable(gmTokenAddress);

        for (uint256 i; i < count; i++) {
            require(
                grailersToken.ownerOf(grailersTokenIds[i]) == a,
                "GrailersToken not owned"
            );
            uint256 tokenId = totalSupply + i;

            bool isUsed = getGrailersTokenUsed(grailersTokenIds[i]);

            require(!isUsed, "GrailersToken already used");

            _setGrailersTokenUsed(grailersTokenIds[i]);

            bytes32 hashOne = createHash(tokenId, msg.sender);
            tokenIdToHash[tokenId] = hashOne;

            _mint(a, tokenId);
        }
    }

    function publicMint(uint256 count, address a) public payable {
        uint256 totalSupply = _owners.length;
        require(project.publicTimetamp < block.timestamp, "Sale not active");
        require(!project.memberOnly, "Only members can mint.");
        require(count > 0, "Mint at least one");
        require(totalSupply + count < project.maxSupply, "Exceeds max supply.");
        require(count < maxPerTx, "Exceeds max per transaction.");
        require(
            count * project.publicPrice <= msg.value,
            "Invalid funds provided."
        );
        require(msg.sender == tx.origin, "No contract minting");

        for (uint256 i; i < count; i++) {
            uint256 tokenId = totalSupply + i;

            bytes32 hashOne = createHash(tokenId, msg.sender);
            tokenIdToHash[tokenId] = hashOne;

            _mint(a, tokenId);
        }
    }

    function createHash(uint256 tokenId, address sender)
        private
        view
        returns (bytes32)
    {
        return
            keccak256(
                abi.encodePacked(
                    tokenId,
                    sender,
                    blockhash(block.number - 2),
                    blockhash(block.number - 4),
                    blockhash(block.number - 8)
                )
            );
    }

    function getHashFromTokenId(uint256 _id) public view returns (bytes32) {
        return tokenIdToHash[_id];
    }

    function _setTokenIdForMembershipId(uint256 _membershipId, uint256 _tokenId)
        private
    {
        uint256 index = _membershipId / 23;
        uint256 bit = (_membershipId % 23) * 11;

        memberShipFlags[index] =
            (memberShipFlags[index] & ~(0x7FF << bit)) |
            (_tokenId << bit);
    }

    function _setGmTokenUsed(uint256 _gmTokenId) private {
        uint256 index = _gmTokenId / 256;
        uint256 bit = _gmTokenId % 256;

        gmTokenFlags[index] = gmTokenFlags[index] | (1 << bit);
    }

    function _setGrailersTokenUsed(uint256 _grailersTokenId) private {
        uint256 index = _grailersTokenId / 256;
        uint256 bit = _grailersTokenId % 256;

        grailersTokenFlags[index] = grailersTokenFlags[index] | (1 << bit);
    }

    function getTokenIdForMembershipId(uint256 _membershipId)
        public
        view
        returns (uint256)
    {
        uint256 index = _membershipId / 23;
        uint256 bit = (_membershipId % 23) * 11;
        uint256 storedValue = (memberShipFlags[index] >> bit) & 0x7FF;
        return storedValue;
    }

    function getMembershipIdForTokenId(uint256 tokenId)
        public
        view
        returns (uint256)
    {
        require(_exists(tokenId), "Token not found");

        uint256[]
            memory allTokenIdsForMembershipIds = getAllTokenIdForMembershipId();

        uint256 membershipId;

        for (uint256 i = 1; i < allTokenIdsForMembershipIds.length; i++) {
            if (allTokenIdsForMembershipIds[i] == tokenId) {
                membershipId = i;
                break;
            }
        }
        return membershipId;
    }

    function getGmTokenUsed(uint256 _gmTokenid) public view returns (bool) {
        uint256 index = _gmTokenid / 256;
        uint256 bit = _gmTokenid % 256;
        bool storedValue = ((gmTokenFlags[index] >> bit) & 1) > 0;
        return storedValue;
    }

    function getGrailersTokenUsed(uint256 _grailersTokenid)
        public
        view
        returns (bool)
    {
        uint256 index = _grailersTokenid / 256;
        uint256 bit = _grailersTokenid % 256;
        bool storedValue = ((grailersTokenFlags[index] >> bit) & 1) > 0;
        return storedValue;
    }

    function getAllTokenIdForMembershipId()
        public
        view
        returns (uint256[] memory)
    {
        uint256[] memory res = new uint256[](4096);
        for (uint256 i = 0; i < 4096; i++) {
            res[i] = getTokenIdForMembershipId(i);
        }
        return res;
    }

    function setBaseURI(string memory _baseURI) public onlyOwner {
        baseURI = _baseURI;
    }

    function setArtistAddress(address payable _artistAddress)
        external
        onlyOwner
    {
        project.artistAddress = _artistAddress;
    }

    function setTwoFiveSixFundsAddress(address payable _twoFiveSixFundsAddress)
        external
        onlyOwner
    {
        project.twoFiveSixFundsAddress = _twoFiveSixFundsAddress;
    }

    function setRoyalty(uint256 _royalty) external onlyOwner {
        project.royalty = _royalty;
    }

    function setRoyaltyAddress(address payable _royaltyAddress)
        external
        onlyOwner
    {
        project.royaltyAddress = _royaltyAddress;
    }

    function setArtScriptAddress(address _artScriptAddress) external onlyOwner {
        project.artScriptAddress = _artScriptAddress;
    }

    function setTwoFiveSixGenesisAddress(address _twoFiveSixGenesisAddress)
        external
        onlyOwner
    {
        twoFiveSixGenesisAddress = _twoFiveSixGenesisAddress;
    }

    function setMemberPrice(uint256 _price) external onlyOwner {
        project.memberPrice = _price;
    }

    function setPublicPrice(uint256 _price) external onlyOwner {
        project.publicPrice = _price;
    }

    function withdraw() public onlyOwner {
        uint256 balance = address(this).balance;

        project.twoFiveSixFundsAddress.transfer(
            (balance / 10000) * twoFiveSixShare
        );
        project.artistAddress.transfer(
            (balance / 10000) * (10000 - twoFiveSixShare)
        );
    }

    function walletOfOwner(address _owner)
        public
        view
        returns (uint256[] memory)
    {
        uint256 tokenCount = balanceOf(_owner);
        if (tokenCount == 0) return new uint256[](0);

        uint256[] memory tokensId = new uint256[](tokenCount);
        for (uint256 i; i < tokenCount; i++) {
            tokensId[i] = tokenOfOwnerByIndex(_owner, i);
        }
        return tokensId;
    }

    function batchTransferFrom(
        address _from,
        address _to,
        uint256[] memory _tokenIds
    ) public {
        for (uint256 i = 0; i < _tokenIds.length; i++) {
            transferFrom(_from, _to, _tokenIds[i]);
        }
    }

    function batchSafeTransferFrom(
        address _from,
        address _to,
        uint256[] memory _tokenIds,
        bytes memory data_
    ) public {
        for (uint256 i = 0; i < _tokenIds.length; i++) {
            safeTransferFrom(_from, _to, _tokenIds[i], data_);
        }
    }

    function isOwnerOf(address account, uint256[] calldata _tokenIds)
        external
        view
        returns (bool)
    {
        for (uint256 i; i < _tokenIds.length; ++i) {
            if (_owners[_tokenIds[i]] != account) return false;
        }

        return true;
    }

    function _mint(address to, uint256 tokenId) internal virtual override {
        _owners.push(to);
        emit Transfer(address(0), to, tokenId);
    }

    function royaltyInfo(uint256, uint256 _salePrice)
        external
        view
        returns (address receiver, uint256 royaltyAmount)
    {
        return (project.royaltyAddress, (_salePrice * project.royalty) / 10000);
    }

    function toHex16(bytes16 data) internal pure returns (bytes32 result) {
        result =
            (bytes32(data) &
                0xFFFFFFFFFFFFFFFF000000000000000000000000000000000000000000000000) |
            ((bytes32(data) &
                0x0000000000000000FFFFFFFFFFFFFFFF00000000000000000000000000000000) >>
                64);
        result =
            (result &
                0xFFFFFFFF000000000000000000000000FFFFFFFF000000000000000000000000) |
            ((result &
                0x00000000FFFFFFFF000000000000000000000000FFFFFFFF0000000000000000) >>
                32);
        result =
            (result &
                0xFFFF000000000000FFFF000000000000FFFF000000000000FFFF000000000000) |
            ((result &
                0x0000FFFF000000000000FFFF000000000000FFFF000000000000FFFF00000000) >>
                16);
        result =
            (result &
                0xFF000000FF000000FF000000FF000000FF000000FF000000FF000000FF000000) |
            ((result &
                0x00FF000000FF000000FF000000FF000000FF000000FF000000FF000000FF0000) >>
                8);
        result =
            ((result &
                0xF000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000) >>
                4) |
            ((result &
                0x0F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F00) >>
                8);
        result = bytes32(
            0x3030303030303030303030303030303030303030303030303030303030303030 +
                uint256(result) +
                (((uint256(result) +
                    0x0606060606060606060606060606060606060606060606060606060606060606) >>
                    4) &
                    0x0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F) *
                7
        );
    }

    function _toLower(string memory str) internal pure returns (string memory) {
        bytes memory bStr = bytes(str);
        bytes memory bLower = new bytes(bStr.length);
        for (uint256 i = 0; i < bStr.length; i++) {
            // Uppercase character...
            if ((uint8(bStr[i]) >= 65) && (uint8(bStr[i]) <= 90)) {
                // So we add 32 to make it lowercase
                bLower[i] = bytes1(uint8(bStr[i]) + 32);
            } else {
                bLower[i] = bStr[i];
            }
        }
        return string(bLower);
    }

    function toHex(bytes32 data) internal pure returns (string memory) {
        return
            string(
                abi.encodePacked(
                    "0x",
                    toHex16(bytes16(data)),
                    toHex16(bytes16(data << 128))
                )
            );
    }

    function getArtFromChain(uint256 tokenId)
        external
        view
        returns (string memory artwork)
    {
        require(_exists(tokenId), "Token not found");

        uint256 membershipId = getMembershipIdForTokenId(tokenId);

        IArtScript artscript = IArtScript(project.artScriptAddress);

        return
            string(
                abi.encodePacked(
                    "data:text/html;base64,",
                    Base64Upgradeable.encode(
                        abi.encodePacked(
                            "<html><head><script>let inputData={'tokenId': ",
                            StringsUpgradeable.toString(tokenId),
                            ",'membershipId': ",
                            StringsUpgradeable.toString(membershipId),
                            ",'hash': '",
                            toHex(getHashFromTokenId(tokenId)),
                            "'}</script>",
                            artscript.head(),
                            "</head><body><script src='",
                            artscript.externalLibrary(),
                            "'></script>",
                            "<script src='",
                            artscript.twoFiveSixLibrary(),
                            "'></script><script defer>",
                            artscript.artScript(),
                            "</script></body></html>"
                        )
                    )
                )
            );
    }

    //convenience project getters
    // Getter function for the name field of a private Project struct
    function projectName() external view returns (string memory) {
        return project.name;
    }

    // Getter function for the artistAddress field of a private Project struct
    function artistAddress() external view returns (address payable) {
        return project.artistAddress;
    }

    // Getter function for the twoFiveSixFundsAddress field of a private Project struct
    function twoFiveSixFundsAddress() external view returns (address payable) {
        return project.twoFiveSixFundsAddress;
    }

    // Getter function for the artScriptAddress field of a private Project struct
    function artScriptAddress() external view returns (address) {
        return project.artScriptAddress;
    }

    // Getter function for the royaltyAddress field of a private Project struct
    function royaltyAddress() external view returns (address) {
        return project.royaltyAddress;
    }

    // Getter function for the maxSupply field of a private Project struct
    function maxSupply() external view returns (uint256) {
        return project.maxSupply;
    }

    // Getter function for the showCaseAmount field of a private Project struct
    function showCaseAmount() external view returns (uint256) {
        return project.showCaseAmount;
    }

    // Getter function for the memberPrice field of a private Project struct
    function memberPrice() external view returns (uint256) {
        return project.memberPrice;
    }

    // Getter function for the publicPrice field of a private Project struct
    function publicPrice() external view returns (uint256) {
        return project.publicPrice;
    }

    // Getter function for the royalty field of a private Project struct
    function royalty() external view returns (uint256) {
        return project.royalty;
    }

    // Getter function for the preSaleTimeStamp field of a private Project struct
    function preSaleTimeStamp() external view returns (uint256) {
        return project.preSaleTimeStamp;
    }

    // Getter function for the publicTimetamp field of a private Project struct
    function publicTimetamp() external view returns (uint256) {
        return project.publicTimetamp;
    }

    // Getter function for the memberOnly field of a private Project struct
    function memberOnly() external view returns (bool) {
        return project.memberOnly;
    }
}

interface IArtScript {
    function projectName() external pure returns (string memory);

    function artistName() external pure returns (string memory);

    function externalLibrary() external pure returns (string memory);

    function twoFiveSixLibrary() external pure returns (string memory);

    function license() external pure returns (string memory);

    function artScript() external pure returns (string memory);

    function head() external pure returns (string memory);
}

// File: contracts/helpers/OwnableUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/Ownable.sol)

pragma solidity ^0.8.13;

import "@openzeppelin/contracts-upgradeable/utils/ContextUpgradeable.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 OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;

    event OwnershipTransferred(
        address indexed previousOwner,
        address indexed newOwner
    );

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init(address _ownerOnInit) internal onlyInitializing {
        __Ownable_init_unchained(_ownerOnInit);
    }

    function __Ownable_init_unchained(address _ownerOnInit)
        internal
        onlyInitializing
    {
        _transferOwnership(_ownerOnInit);
    }

    /**
     * @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);
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}

// File: contracts/helpers/ERC721EnumerableUpgradeable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.13;

import "./ERC721Upgradeable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC721/extensions/IERC721EnumerableUpgradeable.sol";

/**
 * @dev This implements an optional extension of {ERC721} defined in the EIP that adds
 * enumerability of all the token ids in the contract as well as all token ids owned by each
 * account but rips out the core of the gas-wasting processing that comes from OpenZeppelin.
 */
abstract contract ERC721EnumerableUpgradeable is
    ERC721Upgradeable,
    IERC721EnumerableUpgradeable
{
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId)
        public
        view
        virtual
        override(IERC165Upgradeable, ERC721Upgradeable)
        returns (bool)
    {
        return
            interfaceId == type(IERC721EnumerableUpgradeable).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721Enumerable-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _owners.length;
    }

    /**
     * @dev See {IERC721Enumerable-tokenByIndex}.
     */
    function tokenByIndex(uint256 index)
        public
        view
        virtual
        override
        returns (uint256)
    {
        require(
            index < _owners.length,
            "ERC721Enumerable: global index out of bounds"
        );
        return index;
    }

    /**
     * @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index)
        public
        view
        virtual
        override
        returns (uint256 tokenId)
    {
        require(
            index < balanceOf(owner),
            "ERC721Enumerable: owner index out of bounds"
        );

        uint256 count;
        for (uint256 i; i < _owners.length; i++) {
            if (owner == _owners[i]) {
                if (count == index) return i;
                else count++;
            }
        }

        revert("ERC721Enumerable: owner index out of bounds");
    }
}

// File: @openzeppelin/contracts-upgradeable/utils/Base64Upgradeable.sol



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

pragma solidity ^0.8.0;

/**
 * @dev Provides a set of functions to operate with Base64 strings.
 *
 * _Available since v4.5._
 */
library Base64Upgradeable {
    /**
     * @dev Base64 Encoding/Decoding Table
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";

    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal pure returns (string memory) {
        /**
         * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
         * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
         */
        if (data.length == 0) return "";

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

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

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

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

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

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

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

                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
            }

            // When data `bytes` is not exactly 3 bytes long
            // it is padded with `=` characters at the end
            switch mod(mload(data), 3)
            case 1 {
                mstore8(sub(resultPtr, 1), 0x3d)
                mstore8(sub(resultPtr, 2), 0x3d)
            }
            case 2 {
                mstore8(sub(resultPtr, 1), 0x3d)
            }
        }

        return result;
    }
}

// File: @openzeppelin/contracts-upgradeable/utils/ContextUpgradeable.sol



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

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @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 ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol



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

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Internal function that returns the initialized version. Returns `_initialized`
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

    /**
     * @dev Internal function that returns the initialized version. Returns `_initializing`
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}

// File: @openzeppelin/contracts-upgradeable/utils/AddressUpgradeable.sol



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

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

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

// File: contracts/helpers/ERC721Upgradeable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.13;

import "@openzeppelin/contracts-upgradeable/token/ERC721/IERC721Upgradeable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC721/IERC721ReceiverUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC721/extensions/IERC721MetadataUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/ContextUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/StringsUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/introspection/ERC165Upgradeable.sol";
import "./Address.sol";

abstract contract ERC721Upgradeable is
    ContextUpgradeable,
    ERC165Upgradeable,
    IERC721Upgradeable,
    IERC721MetadataUpgradeable
{
    using Address for address;
    using StringsUpgradeable for uint256;

    string private _name;
    string private _symbol;

    // Mapping from token ID to owner address
    address[] internal _owners;

    mapping(uint256 => address) private _tokenApprovals;
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    function __ERC721_init(string memory name_, string memory symbol_)
        internal
        onlyInitializing
    {
        __ERC721_init_unchained(name_, symbol_);
    }

    function __ERC721_init_unchained(string memory name_, string memory symbol_)
        internal
        onlyInitializing
    {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId)
        public
        view
        virtual
        override(ERC165Upgradeable, IERC165Upgradeable)
        returns (bool)
    {
        return
            interfaceId == type(IERC721Upgradeable).interfaceId ||
            interfaceId == type(IERC721MetadataUpgradeable).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner)
        public
        view
        virtual
        override
        returns (uint256)
    {
        require(
            owner != address(0),
            "ERC721: balance query for the zero address"
        );

        uint256 count;
        for (uint256 i; i < _owners.length; ++i) {
            if (owner == _owners[i]) ++count;
        }
        return count;
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        address owner = _owners[tokenId];
        require(
            owner != address(0),
            "ERC721: owner query for nonexistent token"
        );
        return owner;
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ERC721Upgradeable.ownerOf(tokenId);
        require(to != owner, "ERC721: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721: approve caller is not owner nor approved for all"
        );

        _approve(to, tokenId);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        require(
            _exists(tokenId),
            "ERC721: approved query for nonexistent token"
        );

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved)
        public
        virtual
        override
    {
        require(operator != _msgSender(), "ERC721: approve to caller");

        _operatorApprovals[_msgSender()][operator] = approved;
        emit ApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator)
        public
        view
        virtual
        override
        returns (bool)
    {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        //solhint-disable-next-line max-line-length
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721: transfer caller is not owner nor approved"
        );

        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) public virtual override {
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721: transfer caller is not owner nor approved"
        );
        _safeTransfer(from, to, tokenId, _data);
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * `_data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) internal virtual {
        _transfer(from, to, tokenId);
        require(
            _checkOnERC721Received(from, to, tokenId, _data),
            "ERC721: transfer to non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return tokenId < _owners.length && _owners[tokenId] != address(0);
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId)
        internal
        view
        virtual
        returns (bool)
    {
        require(
            _exists(tokenId),
            "ERC721: operator query for nonexistent token"
        );
        address owner = ERC721Upgradeable.ownerOf(tokenId);
        return (spender == owner ||
            getApproved(tokenId) == spender ||
            isApprovedForAll(owner, spender));
    }

    /**
     * @dev Safely mints `tokenId` and transfers it to `to`.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal virtual {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(
        address to,
        uint256 tokenId,
        bytes memory _data
    ) internal virtual {
        _mint(to, tokenId);
        require(
            _checkOnERC721Received(address(0), to, tokenId, _data),
            "ERC721: transfer to non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal virtual {
        require(to != address(0), "ERC721: mint to the zero address");
        require(!_exists(tokenId), "ERC721: token already minted");

        _beforeTokenTransfer(address(0), to, tokenId);
        _owners.push(to);

        emit Transfer(address(0), to, tokenId);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal virtual {
        address owner = ERC721Upgradeable.ownerOf(tokenId);

        _beforeTokenTransfer(owner, address(0), tokenId);

        // Clear approvals
        _approve(address(0), tokenId);
        _owners[tokenId] = address(0);

        emit Transfer(owner, address(0), tokenId);
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {
        require(
            ERC721Upgradeable.ownerOf(tokenId) == from,
            "ERC721: transfer of token that is not own"
        );
        require(to != address(0), "ERC721: transfer to the zero address");

        _beforeTokenTransfer(from, to, tokenId);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId);
        _owners[tokenId] = to;

        emit Transfer(from, to, tokenId);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits a {Approval} event.
     */
    function _approve(address to, uint256 tokenId) internal virtual {
        _tokenApprovals[tokenId] = to;
        emit Approval(ERC721Upgradeable.ownerOf(tokenId), to, tokenId);
    }

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param _data bytes optional data to send along with the call
     * @return bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) private returns (bool) {
        if (to.isContract()) {
            try
                IERC721ReceiverUpgradeable(to).onERC721Received(
                    _msgSender(),
                    from,
                    tokenId,
                    _data
                )
            returns (bytes4 retval) {
                return
                    retval ==
                    IERC721ReceiverUpgradeable.onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert(
                        "ERC721: transfer to non ERC721Receiver implementer"
                    );
                } else {
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting
     * and burning.
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
     * transferred to `to`.
     * - When `from` is zero, `tokenId` will be minted for `to`.
     * - When `to` is zero, ``from``'s `tokenId` will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {}
}

// File: @openzeppelin/contracts-upgradeable/token/ERC721/extensions/IERC721EnumerableUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/extensions/IERC721Enumerable.sol)

pragma solidity ^0.8.0;

import "../IERC721Upgradeable.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721EnumerableUpgradeable is IERC721Upgradeable {
    /**
     * @dev Returns the total amount of tokens stored by the contract.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns a token ID owned by `owner` at a given `index` of its token list.
     * Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index) external view returns (uint256);

    /**
     * @dev Returns a token ID at a given `index` of all the tokens stored by the contract.
     * Use along with {totalSupply} to enumerate all tokens.
     */
    function tokenByIndex(uint256 index) external view returns (uint256);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC721/IERC721Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165Upgradeable.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721Upgradeable is IERC165Upgradeable {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes calldata data
    ) external;

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
     * or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
     * understand this adds an external call which potentially creates a reentrancy vulnerability.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC721/IERC721ReceiverUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721ReceiverUpgradeable {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC721/extensions/IERC721MetadataUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC721Upgradeable.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721MetadataUpgradeable is IERC721Upgradeable {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the token collection symbol.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

// File: @openzeppelin/contracts-upgradeable/utils/StringsUpgradeable.sol



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

pragma solidity ^0.8.0;

import "./math/MathUpgradeable.sol";

/**
 * @dev String operations.
 */
library StringsUpgradeable {
    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 = MathUpgradeable.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, MathUpgradeable.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-upgradeable/utils/introspection/ERC165Upgradeable.sol



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

pragma solidity ^0.8.0;

import "./IERC165Upgradeable.sol";
import "../../proxy/utils/Initializable.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 ERC165Upgradeable is Initializable, IERC165Upgradeable {
    function __ERC165_init() internal onlyInitializing {
    }

    function __ERC165_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165Upgradeable).interfaceId;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}

// File: contracts/helpers/Address.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

library Address {
    function isContract(address account) internal view returns (bool) {
        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 0;
    }
}

// File: @openzeppelin/contracts-upgradeable/utils/introspection/IERC165Upgradeable.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 IERC165Upgradeable {
    /**
     * @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: @openzeppelin/contracts-upgradeable/utils/math/MathUpgradeable.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 MathUpgradeable {
    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);
        }
    }
}