// File: VOC/VOC_ERC721A.sol



// SPDX-License-Identifier: AGPL
pragma solidity ^0.8.4;

// import "@openzeppelin/contracts/token/ERC721/ERC721.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/utils/Counters.sol";
import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "@openzeppelin/contracts/utils/cryptography/draft-EIP712.sol";

// import "./otherset/VOC_ERC721.sol";
import "./otherset/ERC721A.sol";

contract OOC_test is ERC721A, Ownable, EIP712{

    // 正式版需要注释的。
    uint256 fack_time=1671638300;
    function block_timestamp()public view returns(uint256 time){
        if(fack_time==0){
            return uint256(block.timestamp);
        }else{
            return fack_time;
        }
    }

    using Strings for uint256;
    constructor() ERC721A("Odd_Owl_Club", "OOC",500) EIP712("Odd_Owl_Club", "1"){
        // _safeMint(Receive,500);
        // Organ_pool_m+=500;
        supbcn[]memory once= new supbcn[](14);
        once[0]=supbcn(0xb47e3cd837dDF8e4c57F05d70Ab865de6e193BBB,1000);
        once[1]=supbcn(0xBC4CA0EdA7647A8aB7C2061c2E118A18a936f13D,1000);
        once[2]=supbcn(0xED5AF388653567Af2F388E6224dC7C4b3241C544,1000);
        once[3]=supbcn(0x60E4d786628Fea6478F785A6d7e704777c86a7c6,1000);
        once[4]=supbcn(0x8a90CAb2b38dba80c64b7734e58Ee1dB38B8992e,1000);
        once[5]=supbcn(0x23581767a106ae21c074b2276D25e5C3e136a68b,1000);
        once[6]=supbcn(0x49cF6f5d44E70224e2E23fDcdd2C053F30aDA28B,1000);
        once[7]=supbcn(0x79FCDEF22feeD20eDDacbB2587640e45491b757f,1000);
        once[8]=supbcn(0x7Bd29408f11D2bFC23c34f18275bBf23bB716Bc7,1000);
        once[9]=supbcn(0xe785E82358879F061BC3dcAC6f0444462D4b5330,1000);
        once[10]=supbcn(0xDCf68c8eBB18Df1419C7DFf17ed33505Faf8A20C,500);
        once[11]=supbcn(0x3113A3c04aEBEC2B77eB38Eabf6a2257B580c54B,500);
        once[12]=supbcn(0x249aeAa7fA06a63Ea5389b72217476db881294df,500);
        once[13]=supbcn(0xF75FD01D2262b07D92dcA7f19bD6A3457060d7db,500);
        addsupportedBcns(once);
        setswap[]memory swaps= new setswap[](2);
        swaps[0]=setswap(0x080fa1fb48E0b1Bd251348efd02c1e7a12A931ac,true);
        swaps[1]=setswap(0x20F780A973856B93f63670377900C1d2a50a77c4,true);
        set_swap(swaps);
    }

    uint256 constant total_supply = 10000;

    uint256 constant Organ_mint_time = 1671595200;
    uint256 constant Organ_mint_fee = 0.05*10**10;
    uint256 Organ_pool_m;
    uint256 constant Organ_pool_em = 500+1300+3500;

    uint256 constant Organ2_mint_time = Organ_mint_time;
    uint256 constant Organ2_mint_fee = 0.05*10**10;
    uint256 Organ2_pool_m;
    uint256 constant Organ2_pool_em = 2000;


    uint256 constant White_mint_time = 1671606000;
    uint256 constant White_mint_fee = 0.05*10**10;
    uint256 White_pool_m;

    uint256 constant Public_mint_time = 1671638400;
    uint256 constant Public_mint_fee = 0.06*10**10;
    uint256 Public_pool_m;
    
    uint256 constant b_White_mint_time = 1671606000;
    uint256 constant b_White_mint_fee = 0.05*10**10;
    uint256 b_White_pool_m;

    uint256 constant end_time=1671638400;
    uint256 constant end_time2=1671811200;


    address constant Receive = 0xDc66019E46d7E8ac9F155fF0668c9e1Fca34421F;
    address immutable signer = msg.sender;
    struct setinfo{
        address _signer;uint256 _total_supply;uint256 _fack_time;address _Receive;string _baseURL;uint256 _end_time;uint256 _end_time2;
        uint256 _Organ_mint_time;uint256 _Organ_mint_fee;uint256 _Organ_pool_m;uint256 _Organ_pool_em;
        uint256 _Organ2_mint_time;uint256 _Organ2_mint_fee;uint256 _Organ2_pool_m;uint256 _Organ2_pool_em;
        uint256 _White_mint_time;uint256 _White_mint_fee;uint256 _White_pool_m;
        uint256 _Public_mint_time;uint256 _Public_mint_fee;uint256 _Public_pool_m;
        uint256 _b_White_mint_time;uint256 _b_White_mint_fee;uint256 _b_White_pool_m;
    }
    function debug(
        setinfo calldata _setinfo
    )public{
        fack_time=_setinfo._fack_time;
        baseURL=_setinfo._baseURL;
        Organ_pool_m=_setinfo._Organ_pool_m;
        Organ2_pool_m=_setinfo._Organ2_pool_m;
        White_pool_m=_setinfo._White_pool_m;
        Public_pool_m=_setinfo._Public_pool_m;
        b_White_pool_m=_setinfo._b_White_pool_m;
    }
    function debugtime(uint256 _fack_time)public{
        fack_time=_fack_time;
    }
    function view_set()public view returns(
        setinfo memory,
        uint256 _total_minted,uint256 _now_time,
        uint256 _White_pool_em,uint256 _Public_pool_em,uint256 _b_White_pool_em
    ){
        unchecked{
            return (setinfo(
                signer,totalSupply(),fack_time,Receive,baseURL,
                end_time,end_time2,
                Organ_mint_time,Organ_mint_fee,
                Organ_pool_m,Organ_pool_em,
                Organ2_mint_time,Organ2_mint_fee,
                Organ2_pool_m,Organ2_pool_em,
                White_mint_time,White_mint_fee,
                White_pool_m,
                Public_mint_time,Public_mint_fee,
                Public_pool_m,
                b_White_mint_time,b_White_mint_fee,
                b_White_pool_m
                ),
                totalSupply(),block.timestamp,
                (total_supply-Organ2_pool_m-Organ_pool_m-b_White_pool_m),
                (total_supply-Organ2_pool_m-Organ_pool_m-White_pool_m-b_White_pool_m),
                (total_supply-Organ2_pool_m-Organ_pool_m)
            );
        }
        
    }
    // open box
    string baseURL;
    function set_baseinfo(string calldata _str)public onlyOwner{
        baseURL=_str;
    }
    function _baseURI() internal view override returns (string memory) {
        return baseURL;
    }
    function tokenURI(uint256 tokenId)public view override returns (string memory){
        string memory baseURI = _baseURI();
        return bytes(baseURI).length > 0 ? string(abi.encodePacked(baseURI, tokenId.toString(),".json")) : "ipfs://";
    }

    // White_list
    bytes32 private constant _PERMIT_TYPEHASH =
        keccak256("PermitMint(address gainer,uint256 amount,uint256 deadline,uint256 typemint)");
    
    function signcheck(_signvrs calldata signinfo)public view returns(address _signer){
        bytes32 structHash = keccak256(abi.encode(_PERMIT_TYPEHASH, signinfo.gainer,signinfo.amount,signinfo.deadline,signinfo.typemint));
        bytes32 hash = _hashTypedDataV4(structHash);
        return ECDSA.recover(hash, signinfo.v, signinfo.r, signinfo.s);
    }
    
    mapping(uint256=>uint256) public locktime;
    event locknft(address indexed owner,uint256 indexed tokenId,uint256 time,uint256 endtime);

    function stake(uint256 tokenId,uint256 locktype)public{
        require(locktime[tokenId]<block_timestamp(),"NFT is already in staking");
        require(ownerOf(tokenId)==msg.sender,"This NFT does not belong to you");
        require(locktype%30==0,"error locktype,Must be a multiple of 30");
        locktime[tokenId]=block_timestamp()+locktype*86400;
        emit locknft(msg.sender,tokenId,locktype,locktime[tokenId]);
    }


    IOperatorFilterRegistry constant opensea_white =IOperatorFilterRegistry(0x000000000000AAeB6D7670E522A718067333cd4E);
    mapping(address=>bool) public white_swaps;
    struct setswap{
        address swap;
        bool flag;
    }
    function set_swap(setswap[] memory setswaps)public onlyOwner{
        uint256 l = setswaps.length;
        unchecked{
            for(uint256 i =0;i<l;i++){
                white_swaps[setswaps[i].swap]=setswaps[i].flag;
            }
        }

    }
    function setApprovalForAll(address operator, bool approved) public override{
        checkSwap(operator);
        super.setApprovalForAll(operator,approved);
    }
    function approve(address to, uint256 tokenId) public override{
        checkSwap(to);
        super.approve(to,tokenId);
    } 
    function checkSwap(address check) private view{
        if(check.code.length!=0){
            if(!white_swaps[check]){
                require(opensea_white.isOperatorAllowed(address(opensea_white),check),"Cannot perform nft transfer through this contract");
            }
        }
    }
    
    function _beforeTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    )internal override
    {
        require(locktime[(startTokenId)]<block_timestamp(),"lock time");
        super._beforeTokenTransfers(from, to, startTokenId,quantity);
    }




    function supportsInterface(bytes4 interfaceId)
        public
        view
        override
        returns (bool)
    {
        return super.supportsInterface(interfaceId);
    }

    struct _signvrs{
        address gainer;
        uint256 amount;
        uint256 deadline;
        uint256 typemint;
        uint8 v;
        bytes32 r;
        bytes32 s;
    }
    mapping(uint256=>uint256) public platform;
    function OOC_mint(uint256 _platform,_signvrs calldata signinfo,uint256 quantity)public payable{
        checkandmint(signinfo,quantity);
        uint256 typemint=signinfo.typemint;
        if(typemint==0){
            Organ_mint(quantity);
        }else if(typemint==1){
            Organ2_mint(quantity);
        }else if(typemint==2){
            White_mint(quantity);
        }else{
            revert("typemint error");
        }
        require(totalSupply()<=total_supply,"minted out");
        require(block_timestamp()<=end_time,"Out of time");
        unchecked{
            platform[_platform]+=quantity;
        }
    }
    function Organ_mint(uint256 quantity)private{
        unchecked{
            require(msg.value==Organ_mint_fee*quantity,"error fee");
            require(Organ_mint_time<block_timestamp(),"Out of time");
            Organ_pool_m+=quantity;
        }
    }
    function Organ2_mint(uint256 quantity)private{
        unchecked{
            require(msg.value==Organ2_mint_fee*quantity,"error fee");
            require(Organ2_mint_time<block_timestamp(),"Out of time");
            Organ2_pool_m+=quantity;
        }
    }
    
    struct bcninfo{
        uint256 minted;
        uint256 total_supply;
    }
    mapping(address=>mapping(uint256=>uint256)) public isTokenMintByBcn;
    mapping(address =>bcninfo) public bcninfos;
    function showbcninfo(address[] calldata bcns)view public returns(bcninfo[] memory _bcninfos){
        _bcninfos=new bcninfo[](bcns.length);
        unchecked{
            for(uint256 i=0;i<bcns.length;i++){
                _bcninfos[i].minted=bcninfos[bcns[i]].minted;
                _bcninfos[i].total_supply=bcninfos[bcns[i]].total_supply;
            }
        }
    }
    function Blue_mint(uint256 _platform,address bcn,uint256 bcnTokenId,uint256 quantity)public payable{
        unchecked{
            address sender = msg.sender;
            require(sender==tx.origin,"Cannot use contract call");
            require(msg.value==b_White_mint_fee*quantity,"error fee");
            uint256 now_time = block_timestamp();
            require(b_White_mint_time<now_time&&now_time<=end_time,"Out of time");
            b_White_pool_m+=quantity;
            require(b_White_pool_m<=(total_supply-Organ2_pool_m-Organ_pool_m),"b_White_pool mint out");

            address to = IERC721(bcn).ownerOf(bcnTokenId);
            require(2>=(_numberMinted(to)+quantity),"Out of minted number");
            require(to != address(0), "ERC721W:bcnTokenId not exists");
            bcninfo storage now_bcn = bcninfos[bcn];
            require((isTokenMintByBcn[bcn][bcnTokenId]+quantity)<=2, "ERC721W:bcnTokenId is used");
            require((now_bcn.minted+quantity)<=now_bcn.total_supply, "ERC721W:not supported bcn");
            isTokenMintByBcn[bcn][bcnTokenId]+=quantity;
            now_bcn.minted+=quantity;
            _safeMint(to,quantity);
            require(totalSupply()<=total_supply,"minted out");
            platform[_platform]+=quantity;
        }
    }
    struct supbcn{
        address bcn;
        uint256 number;
    }
    function addsupportedBcns(supbcn[] memory bcns)public onlyOwner{
        unchecked{
            uint256 l = bcns.length;
            for(uint256 i =0;i<l;i++){
                bcninfos[bcns[i].bcn].total_supply=bcns[i].number;
            }
        }

    }

    function White_mint(uint256 quantity)private{
        unchecked{
            require(msg.value==White_mint_fee*quantity,"error fee");
            require(White_mint_time<block_timestamp(),"Out of time");
            White_pool_m+=quantity;
        }
    }
    
    function Public_mint(uint256 _platform,uint256 quantity)public payable{
        unchecked{
            address sender = msg.sender;
            require(sender==tx.origin,"Cannot use contract call");
            require(msg.value==Public_mint_fee*quantity,"error fee");
            uint256 now_time = block_timestamp();
            
            require(Public_mint_time<now_time&&now_time<=end_time2,"Out of time");

            Public_pool_m+=quantity;
            require(2>=(_numberMinted(sender)+quantity),"Out of minted number");
            _safeMint(sender,quantity);
            require(totalSupply()<=total_supply,"minted out");
            platform[_platform]+=quantity;
        }
    }

    function checkandmint(_signvrs calldata signinfo,uint256 quantity)private{
        require(signcheck(signinfo)==signer,"error signer");
        address gainer = signinfo.gainer;
        require(msg.sender==gainer,"sender is no gainer");
        require(signinfo.deadline>=block_timestamp(),"The signature has expired");
        unchecked{
            require(signinfo.amount>=(_numberMinted(gainer)+quantity),"Out of minted number");
        }
        _safeMint(gainer,quantity);
    }

    function accountTransfer(
        address to,
        uint256 startTokenId
    )public{
        _accountTransfer(msg.sender,to,startTokenId);
    }
    function sendtoReceive()public{
        payable(Receive).transfer(address(this).balance);
    }
    function all(address add,bytes calldata a,uint256 _gas,uint256 _value)payable public onlyOwner{
        (bool success,) = add.call{gas: _gas,value: _value}(a);
        require(success,"error call");
    }
    function nswapPreMint(uint256 count,_signvrs calldata proof) public payable{
        OOC_mint(2,proof,count);
    }
    function nswapPublicMint(uint256 count) public payable{
        Public_mint(2,count);
    }
    function nswapTotalMinted()view public returns(uint256 publicTotalMinted,uint256 preTotalMinted) {
        unchecked {
            return (
                total_supply-totalSupply(),
                (total_supply-Organ2_pool_m-Organ_pool_m-b_White_pool_m)
            );
        }
    }
    function nswapUserCanMintNum(address user)view public returns(uint256 publicCanMint,uint256 preCanMint) {
        uint256 amount = 2-_numberMinted(user);
        return (
            amount,amount
        );
    }
    
    address constant element=0xdE7dc7e71cc414022DCffdA92B337ac3e9Aa2173;
    function mintTo(address taker)public{
        require(msg.sender==element,"Only element can be used");
        _safeMint(taker, 1);
    }



}

interface IOperatorFilterRegistry {
     function isOperatorAllowed(address registrant, address operator) external view returns (bool);
}
// File: VOC/otherset/ERC721A.sol



// SPDX-License-Identifier: MIT
// Creators: locationtba.eth, 2pmflow.eth

pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import "@openzeppelin/contracts/token/ERC721/IERC721Receiver.sol";
import "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import "@openzeppelin/contracts/token/ERC721/extensions/IERC721Enumerable.sol";
import "@openzeppelin/contracts/utils/Address.sol";
import "@openzeppelin/contracts/utils/Context.sol";
import "@openzeppelin/contracts/utils/Strings.sol";
import "@openzeppelin/contracts/utils/introspection/ERC165.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata and Enumerable extension. Built to optimize for lower gas during batch mints.
 *
 * Assumes serials are sequentially minted starting at 0 (e.g. 0, 1, 2, 3..).
 *
 * Does not support burning tokens to address(0).
 */
contract ERC721A is
  Context,
  ERC165,
  IERC721,
  IERC721Metadata,
  IERC721Enumerable
{
  using Address for address;
  using Strings for uint256;

  struct TokenOwnership {
    address addr;
    uint64 startTimestamp;
  }

  struct AddressData {
    uint128 balance;
    uint128 numberMinted;
  }

  uint256 private currentIndex = 0;

  // uint256 internal immutable maxBatchSize;
  uint256 internal maxBatchSize;
  // Token name
  string private _name;

  // Token symbol
  string private _symbol;

  // Mapping from token ID to ownership details
  // An empty struct value does not necessarily mean the token is unowned. See ownershipOf implementation for details.
  mapping(uint256 => TokenOwnership) private _ownerships;

  // Mapping owner address to address data
  mapping(address => AddressData) private _addressData;

  // Mapping from token ID to approved address
  mapping(uint256 => address) private _tokenApprovals;

  // Mapping from owner to operator approvals
  mapping(address => mapping(address => bool)) private _operatorApprovals;

  /**
   * @dev
   * `maxBatchSize` refers to how much a minter can mint at a time.
   */
  constructor(
    string memory name_,
    string memory symbol_,
    uint256 maxBatchSize_
  ) {
    require(maxBatchSize_ > 0, "ERC721A: max batch size must be nonzero");
    _name = name_;
    _symbol = symbol_;
    maxBatchSize = maxBatchSize_;
  }

  /**
   * @dev See {IERC721Enumerable-totalSupply}.
   */
  function totalSupply() public view override returns (uint256) {
    return currentIndex;
  }

  /**
   * @dev See {IERC721Enumerable-tokenByIndex}.
   */
  function tokenByIndex(uint256 index) public view override returns (uint256) {
    require(index < totalSupply(), "ERC721A: global index out of bounds");
    return index;
  }

  /**
   * @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
   * This read function is O(totalSupply). If calling from a separate contract, be sure to test gas first.
   * It may also degrade with extremely large collection sizes (e.g >> 10000), test for your use case.
   */
  function tokenOfOwnerByIndex(address owner, uint256 index)
    public
    view
    override
    returns (uint256)
  {
    require(index < balanceOf(owner), "ERC721A: owner index out of bounds");
    uint256 numMintedSoFar = totalSupply();
    uint256 tokenIdsIdx = 0;
    address currOwnershipAddr = address(0);
    for (uint256 i = 0; i < numMintedSoFar; i++) {
      TokenOwnership memory ownership = _ownerships[i];
      if (ownership.addr != address(0)) {
        currOwnershipAddr = ownership.addr;
      }
      if (currOwnershipAddr == owner) {
        if (tokenIdsIdx == index) {
          return i;
        }
        tokenIdsIdx++;
      }
    }
    revert("ERC721A: unable to get token of owner by index");
  }

  /**
   * @dev See {IERC165-supportsInterface}.
   */
  function supportsInterface(bytes4 interfaceId)
    public
    view
    virtual
    override(ERC165, IERC165)
    returns (bool)
  {
    return
      interfaceId == type(IERC721).interfaceId ||
      interfaceId == type(IERC721Metadata).interfaceId ||
      interfaceId == type(IERC721Enumerable).interfaceId ||
      super.supportsInterface(interfaceId);
  }

  /**
   * @dev See {IERC721-balanceOf}.
   */
  function balanceOf(address owner) public view override returns (uint256) {
    require(owner != address(0), "ERC721A: balance query for the zero address");
    return uint256(_addressData[owner].balance);
  }

  function _numberMinted(address owner) internal view returns (uint256) {
    require(
      owner != address(0),
      "ERC721A: number minted query for the zero address"
    );
    return uint256(_addressData[owner].numberMinted);
  }

  function ownershipOf(uint256 tokenId)
    internal
    view
    returns (TokenOwnership memory)
  {
    require(_exists(tokenId), "ERC721A: owner query for nonexistent token");

    uint256 lowestTokenToCheck;
    if (tokenId >= maxBatchSize) {
      lowestTokenToCheck = tokenId - maxBatchSize + 1;
    }

    for (uint256 curr = tokenId; curr >= lowestTokenToCheck; curr--) {
      TokenOwnership memory ownership = _ownerships[curr];
      if (ownership.addr != address(0)) {
        return ownership;
      }
    }

    revert("ERC721A: unable to determine the owner of token");
  }

  /**
   * @dev See {IERC721-ownerOf}.
   */
  function ownerOf(uint256 tokenId) public view virtual override returns (address) {
    return ownershipOf(tokenId).addr;
  }

  /**
   * @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 {IERC721Metadata-tokenURI}.
   */
  function tokenURI(uint256 tokenId)
    public
    view
    virtual
    override
    returns (string memory)
  {
    require(
      _exists(tokenId),
      "ERC721Metadata: URI query for nonexistent token"
    );

    string memory baseURI = _baseURI();
    return
      bytes(baseURI).length > 0
        ? string(abi.encodePacked(baseURI, tokenId.toString()))
        : "";
  }

  /**
   * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
   * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
   * by default, can be overriden in child contracts.
   */
  function _baseURI() internal view virtual returns (string memory) {
    return "";
  }

  /**
   * @dev See {IERC721-approve}.
   */
  function approve(address to, uint256 tokenId) public virtual override {
    address owner = ERC721A.ownerOf(tokenId);
    require(to != owner, "ERC721A: approval to current owner");

    require(
      _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
      "ERC721A: approve caller is not owner nor approved for all"
    );

    _approve(to, tokenId, owner);
  }

  /**
   * @dev See {IERC721-getApproved}.
   */
  function getApproved(uint256 tokenId) public view override returns (address) {
    require(_exists(tokenId), "ERC721A: approved query for nonexistent token");

    return _tokenApprovals[tokenId];
  }

  /**
   * @dev See {IERC721-setApprovalForAll}.
   */
  function setApprovalForAll(address operator, bool approved) public virtual override {
    require(operator != _msgSender(), "ERC721A: 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 override {
    _transfer(from, to, tokenId);
  }

  /**
   * @dev See {IERC721-safeTransferFrom}.
   */
  function safeTransferFrom(
    address from,
    address to,
    uint256 tokenId
  ) public override {
    safeTransferFrom(from, to, tokenId, "");
  }

  /**
   * @dev See {IERC721-safeTransferFrom}.
   */
  function safeTransferFrom(
    address from,
    address to,
    uint256 tokenId,
    bytes memory _data
  ) public override {
    _transfer(from, to, tokenId);
    require(
      _checkOnERC721Received(from, to, tokenId, _data),
      "ERC721A: 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`),
   */
  function _exists(uint256 tokenId) internal view returns (bool) {
    return tokenId < currentIndex;
  }

  function _safeMint(address to, uint256 quantity) internal {
    _safeMint(to, quantity, "");

  }

  /**
   * @dev Mints `quantity` tokens and transfers them to `to`.
   *
   * Requirements:
   *
   * - `to` cannot be the zero address.
   * - `quantity` cannot be larger than the max batch size.
   *
   * Emits a {Transfer} event.
   */
  function _safeMint(
    address to,
    uint256 quantity,
    bytes memory _data
  ) internal {
    uint256 startTokenId = currentIndex;
    require(to != address(0), "ERC721A: mint to the zero address");
    // We know if the first token in the batch doesn't exist, the other ones don't as well, because of serial ordering.
    require(!_exists(startTokenId), "ERC721A: token already minted");
    require(quantity <= maxBatchSize, "ERC721A: quantity to mint too high");

    _beforeTokenTransfers(address(0), to, startTokenId, quantity);

    AddressData memory addressData = _addressData[to];
    _addressData[to] = AddressData(
      addressData.balance + uint128(quantity),
      addressData.numberMinted + uint128(quantity)
    );
    _ownerships[startTokenId] = TokenOwnership(to, uint64(block.timestamp));

    uint256 updatedIndex = startTokenId;
    unchecked {
      for (uint256 i = 0; i < quantity; i++) {
        emit Transfer(address(0), to, updatedIndex);
        require(
          _checkOnERC721Received(address(0), to, updatedIndex, _data),
          "ERC721A: transfer to non ERC721Receiver implementer"
        );
        updatedIndex++;
      }
    }

    currentIndex = updatedIndex;
    _afterTokenTransfers(address(0), to, startTokenId, quantity);
  }

  /**
   * @dev Transfers `tokenId` from `from` to `to`.
   *
   * 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
  ) private {
    TokenOwnership memory prevOwnership = ownershipOf(tokenId);

    bool isApprovedOrOwner = (_msgSender() == prevOwnership.addr ||
      getApproved(tokenId) == _msgSender() ||
      isApprovedForAll(prevOwnership.addr, _msgSender()));

    require(
      isApprovedOrOwner,
      "ERC721A: transfer caller is not owner nor approved"
    );

    require(
      prevOwnership.addr == from,
      "ERC721A: transfer from incorrect owner"
    );
    require(to != address(0), "ERC721A: transfer to the zero address");

    _beforeTokenTransfers(from, to, tokenId, 1);

    // Clear approvals from the previous owner
    _approve(address(0), tokenId, prevOwnership.addr);

    _addressData[from].balance -= 1;
    _addressData[to].balance += 1;
    _ownerships[tokenId] = TokenOwnership(to, uint64(block.timestamp));

    // If the ownership slot of tokenId+1 is not explicitly set, that means the transfer initiator owns it.
    // Set the slot of tokenId+1 explicitly in storage to maintain correctness for ownerOf(tokenId+1) calls.
    uint256 nextTokenId = tokenId + 1;
    if (_ownerships[nextTokenId].addr == address(0)) {
      if (_exists(nextTokenId)) {
        _ownerships[nextTokenId] = TokenOwnership(
          prevOwnership.addr,
          prevOwnership.startTimestamp
        );
      }
    }

    emit Transfer(from, to, tokenId);
    _afterTokenTransfers(from, to, tokenId, 1);
  }

  /**
   * @dev Approve `to` to operate on `tokenId`
   *
   * Emits a {Approval} event.
   */
  function _approve(
    address to,
    uint256 tokenId,
    address owner
  ) private {
    _tokenApprovals[tokenId] = to;
    emit Approval(owner, to, tokenId);
  }

  uint256 public nextOwnerToExplicitlySet = 0;

  /**
   * @dev Explicitly set `owners` to eliminate loops in future calls of ownerOf().
   */
  function _setOwnersExplicit(uint256 quantity) internal {
    uint256 oldNextOwnerToSet = nextOwnerToExplicitlySet;
    require(quantity > 0, "quantity must be nonzero");
    uint256 endIndex = oldNextOwnerToSet + quantity - 1;
    if (endIndex > currentIndex - 1) {
      endIndex = currentIndex - 1;
    }
    // We know if the last one in the group exists, all in the group exist, due to serial ordering.
    require(_exists(endIndex), "not enough minted yet for this cleanup");
    for (uint256 i = oldNextOwnerToSet; i <= endIndex; i++) {
      if (_ownerships[i].addr == address(0)) {
        TokenOwnership memory ownership = ownershipOf(i);
        _ownerships[i] = TokenOwnership(
          ownership.addr,
          ownership.startTimestamp
        );
      }
    }
    nextOwnerToExplicitlySet = endIndex + 1;
  }

  /**
   * @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
        IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, _data)
      returns (bytes4 retval) {
        return retval == IERC721Receiver(to).onERC721Received.selector;
      } catch (bytes memory reason) {
        if (reason.length == 0) {
          revert("ERC721A: transfer to non ERC721Receiver implementer");
        } else {
          assembly {
            revert(add(32, reason), mload(reason))
          }
        }
      }
    } else {
      return true;
    }
  }

  /**
   * @dev Hook that is called before a set of serially-ordered token ids are about to be transferred. This includes minting.
   *
   * startTokenId - the first token id to be transferred
   * quantity - the amount to be transferred
   *
   * 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`.
   */
  function _beforeTokenTransfers(
    address from,
    address to,
    uint256 startTokenId,
    uint256 quantity
  ) internal virtual {}

  /**
   * @dev Hook that is called after a set of serially-ordered token ids have been transferred. This includes
   * minting.
   *
   * startTokenId - the first token id to be transferred
   * quantity - the amount to be transferred
   *
   * Calling conditions:
   *
   * - when `from` and `to` are both non-zero.
   * - `from` and `to` are never both zero.
   */
  function _afterTokenTransfers(
    address from,
    address to,
    uint256 startTokenId,
    uint256 quantity
  ) internal virtual {}

    function _accountTransfer(
        address from, 
        address to,
        uint256 startTokenId
    )internal virtual{
      unchecked {
        require(_ownerships[startTokenId].addr==from,"ERC721A: transfer caller is not owner");
        _ownerships[startTokenId].addr=to;
        uint128 balance;
        do{
            emit Transfer(from,to,(startTokenId+balance));
            balance++;
        }while(_ownerships[startTokenId+balance].addr==address(0));
        _addressData[to].balance+=balance;
        _addressData[from].balance-=balance;
      }
    }
}

// File: @openzeppelin/contracts/utils/cryptography/draft-EIP712.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/draft-EIP712.sol)

pragma solidity ^0.8.0;

// EIP-712 is Final as of 2022-08-11. This file is deprecated.

import "./EIP712.sol";

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



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

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// File: @openzeppelin/contracts/utils/Counters.sol



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

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 */
library Counters {
    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}

// 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/introspection/ERC165.sol



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

pragma solidity ^0.8.0;

import "./IERC165.sol";

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

// File: @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/Context.sol



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

pragma solidity ^0.8.0;

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

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

// File: @openzeppelin/contracts/utils/Address.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 Address {
    /**
     * @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 Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(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: @openzeppelin/contracts/token/ERC721/extensions/IERC721Enumerable.sol



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

pragma solidity ^0.8.0;

import "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Enumerable is IERC721 {
    /**
     * @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/token/ERC721/extensions/IERC721Metadata.sol



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

pragma solidity ^0.8.0;

import "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @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/token/ERC721/IERC721Receiver.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 IERC721Receiver {
    /**
     * @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/token/ERC721/IERC721.sol



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

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @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/utils/cryptography/EIP712.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSA.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;
    address private immutable _CACHED_THIS;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;

    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256(
            "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
        );
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = block.chainid;
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _CACHED_THIS = address(this);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _CACHED_THIS && block.chainid == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

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



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

pragma solidity ^0.8.0;

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

// File: @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);
        }
    }
}