// File: contracts/Caesar.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import "./DateTime.sol";
import "erc721a/contracts/ERC721A.sol";
import "@openzeppelin/contracts/utils/Strings.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";

contract Caesar is ERC721A, Ownable, ReentrancyGuard {
  uint256 public constant COLLECTION_SIZE = 10000;
  mapping(uint256 => uint256) private _tokenLockedData;
  bool public saleIsActive = false;
  uint256 public preSalePrice = 0;

  constructor() ERC721A("Caesar", "CAESAR") {}

  modifier callerIsUser() {
    require(tx.origin == msg.sender, "Caesar: caller is another contract");
    _;
  }

  function devMint(uint8 _batchSize, uint256 _quantity) external onlyOwner {
    require(
      totalSupply() + _quantity <= COLLECTION_SIZE,
      "Caesar: reached max supply"
    );
    require(
      _quantity % _batchSize == 0,
      "Caesar: can only mint a multiple of the batchSize"
    );

    uint256 numChunks = _quantity / _batchSize;

    for (uint256 i = 0; i < numChunks; i++) {
      _safeMint(msg.sender, _batchSize);
    }
  }

  string private _baseTokenURI;

  function _baseURI() internal view virtual override returns (string memory) {
    return _baseTokenURI;
  }

  function setBaseURI(string calldata baseURI) external onlyOwner {
    _baseTokenURI = baseURI;
  }

  function setSaleActive(
    bool _isActive,
    uint256 _preSalePrice
  ) external onlyOwner {
    saleIsActive = _isActive;
    preSalePrice = (_preSalePrice * 1 ether);
  }

  function setApproveToContract(
    uint256 _min,
    uint256 _max,
    bool _revoke
  ) external onlyOwner {
    require(_min < _max, "Caesar: max must be greater than min");

    for (uint256 numOfToken = _min; numOfToken <= _max; numOfToken++) {
      if (ownerOf(numOfToken) != msg.sender) continue;

      if (_revoke) {
        approve(address(0), numOfToken);
      } else {
        approve(address(this), numOfToken);
      }
    }
  }

  function _beforeTokenTransfers(
    address _from,
    address _to,
    uint256 _startTokenId,
    uint256 _quantity
  ) internal virtual override {
    super._beforeTokenTransfers(_from, _to, _startTokenId, _quantity);

    (uint256 year, uint256 month, uint256 day) = DateTime.timestampToDate(
      _tokenLockedData[_startTokenId]
    );

    string memory stringYear = Strings.toString(year);
    string memory stringMonth = "";
    string memory stringDay = Strings.toString(day);

    if (month == 1) {
      stringMonth = "Jan";
    } else if (month == 2) {
      stringMonth = "Feb";
    } else if (month == 3) {
      stringMonth = "Mar";
    } else if (month == 4) {
      stringMonth = "Apr";
    } else if (month == 5) {
      stringMonth = "Mau";
    } else if (month == 6) {
      stringMonth = "Jun";
    } else if (month == 7) {
      stringMonth = "Jul";
    } else if (month == 8) {
      stringMonth = "Aug";
    } else if (month == 9) {
      stringMonth = "Sep";
    } else if (month == 10) {
      stringMonth = "Oct";
    } else if (month == 11) {
      stringMonth = "Nov";
    } else {
      stringMonth = "Dec";
    }

    string memory message = "Caesar: This token ID cannot be transfer until ";
    message = string.concat(message, stringMonth);
    message = string.concat(message, " ");
    message = string.concat(message, stringDay);
    message = string.concat(message, ", ");
    message = string.concat(message, stringYear);

    require(block.timestamp > _tokenLockedData[_startTokenId], message);
  }

  function gracePeriodOfTransfer(
    address _to,
    uint256 _tokenId,
    uint256 _expiredDays
  ) external onlyOwner {
    safeTransferFrom(msg.sender, _to, _tokenId);

    _tokenLockedData[_tokenId] = block.timestamp + (_expiredDays * 1 days);
  }

  function getTokenLockedData(uint256 _tokenId) public view returns (uint256) {
    return _tokenLockedData[_tokenId];
  }

  function preSale(
    uint256 _tokenId
  ) external payable callerIsUser nonReentrant {
    require(
      saleIsActive && preSalePrice > 0,
      "Caesar: presale have not started yet"
    );
    require(
      ownerOf(_tokenId) == owner() && getApproved(_tokenId) == address(this),
      "Caesar: this token ID cannot be purchased"
    );

    IERC721A(address(this)).safeTransferFrom(owner(), msg.sender, _tokenId);

    refundIfOver(preSalePrice);
  }

  function refundIfOver(uint256 price) private {
    require(msg.value >= price, "Caesar: need to send more ETH");
    if (msg.value > price) {
      payable(msg.sender).transfer(msg.value - price);
    }
  }

  function withdrawMoney() external onlyOwner nonReentrant {
    (bool success, ) = msg.sender.call{value: address(this).balance}("");
    require(success, "Caesar: transfer failed");
  }
}

// File: @openzeppelin/contracts/security/ReentrancyGuard.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == _ENTERED;
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (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. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

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

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

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

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

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

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

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// File: erc721a/contracts/ERC721A.sol



// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.2.3
// Creator: Chiru Labs

pragma solidity ^0.8.4;

import './IERC721A.sol';

/**
 * @dev Interface of ERC721 token receiver.
 */
interface ERC721A__IERC721Receiver {
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

/**
 * @title ERC721A
 *
 * @dev Implementation of the [ERC721](https://eips.ethereum.org/EIPS/eip-721)
 * Non-Fungible Token Standard, including the Metadata extension.
 * Optimized for lower gas during batch mints.
 *
 * Token IDs are minted in sequential order (e.g. 0, 1, 2, 3, ...)
 * starting from `_startTokenId()`.
 *
 * Assumptions:
 *
 * - An owner cannot have more than 2**64 - 1 (max value of uint64) of supply.
 * - The maximum token ID cannot exceed 2**256 - 1 (max value of uint256).
 */
contract ERC721A is IERC721A {
    // Bypass for a `--via-ir` bug (https://github.com/chiru-labs/ERC721A/pull/364).
    struct TokenApprovalRef {
        address value;
    }

    // =============================================================
    //                           CONSTANTS
    // =============================================================

    // Mask of an entry in packed address data.
    uint256 private constant _BITMASK_ADDRESS_DATA_ENTRY = (1 << 64) - 1;

    // The bit position of `numberMinted` in packed address data.
    uint256 private constant _BITPOS_NUMBER_MINTED = 64;

    // The bit position of `numberBurned` in packed address data.
    uint256 private constant _BITPOS_NUMBER_BURNED = 128;

    // The bit position of `aux` in packed address data.
    uint256 private constant _BITPOS_AUX = 192;

    // Mask of all 256 bits in packed address data except the 64 bits for `aux`.
    uint256 private constant _BITMASK_AUX_COMPLEMENT = (1 << 192) - 1;

    // The bit position of `startTimestamp` in packed ownership.
    uint256 private constant _BITPOS_START_TIMESTAMP = 160;

    // The bit mask of the `burned` bit in packed ownership.
    uint256 private constant _BITMASK_BURNED = 1 << 224;

    // The bit position of the `nextInitialized` bit in packed ownership.
    uint256 private constant _BITPOS_NEXT_INITIALIZED = 225;

    // The bit mask of the `nextInitialized` bit in packed ownership.
    uint256 private constant _BITMASK_NEXT_INITIALIZED = 1 << 225;

    // The bit position of `extraData` in packed ownership.
    uint256 private constant _BITPOS_EXTRA_DATA = 232;

    // Mask of all 256 bits in a packed ownership except the 24 bits for `extraData`.
    uint256 private constant _BITMASK_EXTRA_DATA_COMPLEMENT = (1 << 232) - 1;

    // The mask of the lower 160 bits for addresses.
    uint256 private constant _BITMASK_ADDRESS = (1 << 160) - 1;

    // The maximum `quantity` that can be minted with {_mintERC2309}.
    // This limit is to prevent overflows on the address data entries.
    // For a limit of 5000, a total of 3.689e15 calls to {_mintERC2309}
    // is required to cause an overflow, which is unrealistic.
    uint256 private constant _MAX_MINT_ERC2309_QUANTITY_LIMIT = 5000;

    // The `Transfer` event signature is given by:
    // `keccak256(bytes("Transfer(address,address,uint256)"))`.
    bytes32 private constant _TRANSFER_EVENT_SIGNATURE =
        0xddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef;

    // =============================================================
    //                            STORAGE
    // =============================================================

    // The next token ID to be minted.
    uint256 private _currentIndex;

    // The number of tokens burned.
    uint256 private _burnCounter;

    // 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 {_packedOwnershipOf} implementation for details.
    //
    // Bits Layout:
    // - [0..159]   `addr`
    // - [160..223] `startTimestamp`
    // - [224]      `burned`
    // - [225]      `nextInitialized`
    // - [232..255] `extraData`
    mapping(uint256 => uint256) private _packedOwnerships;

    // Mapping owner address to address data.
    //
    // Bits Layout:
    // - [0..63]    `balance`
    // - [64..127]  `numberMinted`
    // - [128..191] `numberBurned`
    // - [192..255] `aux`
    mapping(address => uint256) private _packedAddressData;

    // Mapping from token ID to approved address.
    mapping(uint256 => TokenApprovalRef) private _tokenApprovals;

    // Mapping from owner to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    // =============================================================
    //                          CONSTRUCTOR
    // =============================================================

    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
        _currentIndex = _startTokenId();
    }

    // =============================================================
    //                   TOKEN COUNTING OPERATIONS
    // =============================================================

    /**
     * @dev Returns the starting token ID.
     * To change the starting token ID, please override this function.
     */
    function _startTokenId() internal view virtual returns (uint256) {
        return 0;
    }

    /**
     * @dev Returns the next token ID to be minted.
     */
    function _nextTokenId() internal view virtual returns (uint256) {
        return _currentIndex;
    }

    /**
     * @dev Returns the total number of tokens in existence.
     * Burned tokens will reduce the count.
     * To get the total number of tokens minted, please see {_totalMinted}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        // Counter underflow is impossible as _burnCounter cannot be incremented
        // more than `_currentIndex - _startTokenId()` times.
        unchecked {
            return _currentIndex - _burnCounter - _startTokenId();
        }
    }

    /**
     * @dev Returns the total amount of tokens minted in the contract.
     */
    function _totalMinted() internal view virtual returns (uint256) {
        // Counter underflow is impossible as `_currentIndex` does not decrement,
        // and it is initialized to `_startTokenId()`.
        unchecked {
            return _currentIndex - _startTokenId();
        }
    }

    /**
     * @dev Returns the total number of tokens burned.
     */
    function _totalBurned() internal view virtual returns (uint256) {
        return _burnCounter;
    }

    // =============================================================
    //                    ADDRESS DATA OPERATIONS
    // =============================================================

    /**
     * @dev Returns the number of tokens in `owner`'s account.
     */
    function balanceOf(address owner) public view virtual override returns (uint256) {
        if (owner == address(0)) revert BalanceQueryForZeroAddress();
        return _packedAddressData[owner] & _BITMASK_ADDRESS_DATA_ENTRY;
    }

    /**
     * Returns the number of tokens minted by `owner`.
     */
    function _numberMinted(address owner) internal view returns (uint256) {
        return (_packedAddressData[owner] >> _BITPOS_NUMBER_MINTED) & _BITMASK_ADDRESS_DATA_ENTRY;
    }

    /**
     * Returns the number of tokens burned by or on behalf of `owner`.
     */
    function _numberBurned(address owner) internal view returns (uint256) {
        return (_packedAddressData[owner] >> _BITPOS_NUMBER_BURNED) & _BITMASK_ADDRESS_DATA_ENTRY;
    }

    /**
     * Returns the auxiliary data for `owner`. (e.g. number of whitelist mint slots used).
     */
    function _getAux(address owner) internal view returns (uint64) {
        return uint64(_packedAddressData[owner] >> _BITPOS_AUX);
    }

    /**
     * Sets the auxiliary data for `owner`. (e.g. number of whitelist mint slots used).
     * If there are multiple variables, please pack them into a uint64.
     */
    function _setAux(address owner, uint64 aux) internal virtual {
        uint256 packed = _packedAddressData[owner];
        uint256 auxCasted;
        // Cast `aux` with assembly to avoid redundant masking.
        assembly {
            auxCasted := aux
        }
        packed = (packed & _BITMASK_AUX_COMPLEMENT) | (auxCasted << _BITPOS_AUX);
        _packedAddressData[owner] = packed;
    }

    // =============================================================
    //                            IERC165
    // =============================================================

    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * [EIP section](https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified)
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30000 gas.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        // The interface IDs are constants representing the first 4 bytes
        // of the XOR of all function selectors in the interface.
        // See: [ERC165](https://eips.ethereum.org/EIPS/eip-165)
        // (e.g. `bytes4(i.functionA.selector ^ i.functionB.selector ^ ...)`)
        return
            interfaceId == 0x01ffc9a7 || // ERC165 interface ID for ERC165.
            interfaceId == 0x80ac58cd || // ERC165 interface ID for ERC721.
            interfaceId == 0x5b5e139f; // ERC165 interface ID for ERC721Metadata.
    }

    // =============================================================
    //                        IERC721Metadata
    // =============================================================

    /**
     * @dev Returns the token collection name.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the token collection symbol.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
        if (!_exists(tokenId)) revert URIQueryForNonexistentToken();

        string memory baseURI = _baseURI();
        return bytes(baseURI).length != 0 ? string(abi.encodePacked(baseURI, _toString(tokenId))) : '';
    }

    /**
     * @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, it can be overridden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return '';
    }

    // =============================================================
    //                     OWNERSHIPS OPERATIONS
    // =============================================================

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) public view virtual override returns (address) {
        return address(uint160(_packedOwnershipOf(tokenId)));
    }

    /**
     * @dev Gas spent here starts off proportional to the maximum mint batch size.
     * It gradually moves to O(1) as tokens get transferred around over time.
     */
    function _ownershipOf(uint256 tokenId) internal view virtual returns (TokenOwnership memory) {
        return _unpackedOwnership(_packedOwnershipOf(tokenId));
    }

    /**
     * @dev Returns the unpacked `TokenOwnership` struct at `index`.
     */
    function _ownershipAt(uint256 index) internal view virtual returns (TokenOwnership memory) {
        return _unpackedOwnership(_packedOwnerships[index]);
    }

    /**
     * @dev Initializes the ownership slot minted at `index` for efficiency purposes.
     */
    function _initializeOwnershipAt(uint256 index) internal virtual {
        if (_packedOwnerships[index] == 0) {
            _packedOwnerships[index] = _packedOwnershipOf(index);
        }
    }

    /**
     * Returns the packed ownership data of `tokenId`.
     */
    function _packedOwnershipOf(uint256 tokenId) private view returns (uint256) {
        uint256 curr = tokenId;

        unchecked {
            if (_startTokenId() <= curr)
                if (curr < _currentIndex) {
                    uint256 packed = _packedOwnerships[curr];
                    // If not burned.
                    if (packed & _BITMASK_BURNED == 0) {
                        // Invariant:
                        // There will always be an initialized ownership slot
                        // (i.e. `ownership.addr != address(0) && ownership.burned == false`)
                        // before an unintialized ownership slot
                        // (i.e. `ownership.addr == address(0) && ownership.burned == false`)
                        // Hence, `curr` will not underflow.
                        //
                        // We can directly compare the packed value.
                        // If the address is zero, packed will be zero.
                        while (packed == 0) {
                            packed = _packedOwnerships[--curr];
                        }
                        return packed;
                    }
                }
        }
        revert OwnerQueryForNonexistentToken();
    }

    /**
     * @dev Returns the unpacked `TokenOwnership` struct from `packed`.
     */
    function _unpackedOwnership(uint256 packed) private pure returns (TokenOwnership memory ownership) {
        ownership.addr = address(uint160(packed));
        ownership.startTimestamp = uint64(packed >> _BITPOS_START_TIMESTAMP);
        ownership.burned = packed & _BITMASK_BURNED != 0;
        ownership.extraData = uint24(packed >> _BITPOS_EXTRA_DATA);
    }

    /**
     * @dev Packs ownership data into a single uint256.
     */
    function _packOwnershipData(address owner, uint256 flags) private view returns (uint256 result) {
        assembly {
            // Mask `owner` to the lower 160 bits, in case the upper bits somehow aren't clean.
            owner := and(owner, _BITMASK_ADDRESS)
            // `owner | (block.timestamp << _BITPOS_START_TIMESTAMP) | flags`.
            result := or(owner, or(shl(_BITPOS_START_TIMESTAMP, timestamp()), flags))
        }
    }

    /**
     * @dev Returns the `nextInitialized` flag set if `quantity` equals 1.
     */
    function _nextInitializedFlag(uint256 quantity) private pure returns (uint256 result) {
        // For branchless setting of the `nextInitialized` flag.
        assembly {
            // `(quantity == 1) << _BITPOS_NEXT_INITIALIZED`.
            result := shl(_BITPOS_NEXT_INITIALIZED, eq(quantity, 1))
        }
    }

    // =============================================================
    //                      APPROVAL OPERATIONS
    // =============================================================

    /**
     * @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) public payable virtual override {
        address owner = ownerOf(tokenId);

        if (_msgSenderERC721A() != owner)
            if (!isApprovedForAll(owner, _msgSenderERC721A())) {
                revert ApprovalCallerNotOwnerNorApproved();
            }

        _tokenApprovals[tokenId].value = to;
        emit Approval(owner, to, tokenId);
    }

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) public view virtual override returns (address) {
        if (!_exists(tokenId)) revert ApprovalQueryForNonexistentToken();

        return _tokenApprovals[tokenId].value;
    }

    /**
     * @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) public virtual override {
        _operatorApprovals[_msgSenderERC721A()][operator] = approved;
        emit ApprovalForAll(_msgSenderERC721A(), operator, approved);
    }

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

    /**
     * @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. See {_mint}.
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return
            _startTokenId() <= tokenId &&
            tokenId < _currentIndex && // If within bounds,
            _packedOwnerships[tokenId] & _BITMASK_BURNED == 0; // and not burned.
    }

    /**
     * @dev Returns whether `msgSender` is equal to `approvedAddress` or `owner`.
     */
    function _isSenderApprovedOrOwner(
        address approvedAddress,
        address owner,
        address msgSender
    ) private pure returns (bool result) {
        assembly {
            // Mask `owner` to the lower 160 bits, in case the upper bits somehow aren't clean.
            owner := and(owner, _BITMASK_ADDRESS)
            // Mask `msgSender` to the lower 160 bits, in case the upper bits somehow aren't clean.
            msgSender := and(msgSender, _BITMASK_ADDRESS)
            // `msgSender == owner || msgSender == approvedAddress`.
            result := or(eq(msgSender, owner), eq(msgSender, approvedAddress))
        }
    }

    /**
     * @dev Returns the storage slot and value for the approved address of `tokenId`.
     */
    function _getApprovedSlotAndAddress(uint256 tokenId)
        private
        view
        returns (uint256 approvedAddressSlot, address approvedAddress)
    {
        TokenApprovalRef storage tokenApproval = _tokenApprovals[tokenId];
        // The following is equivalent to `approvedAddress = _tokenApprovals[tokenId].value`.
        assembly {
            approvedAddressSlot := tokenApproval.slot
            approvedAddress := sload(approvedAddressSlot)
        }
    }

    // =============================================================
    //                      TRANSFER OPERATIONS
    // =============================================================

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *
     * 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
    ) public payable virtual override {
        uint256 prevOwnershipPacked = _packedOwnershipOf(tokenId);

        if (address(uint160(prevOwnershipPacked)) != from) revert TransferFromIncorrectOwner();

        (uint256 approvedAddressSlot, address approvedAddress) = _getApprovedSlotAndAddress(tokenId);

        // The nested ifs save around 20+ gas over a compound boolean condition.
        if (!_isSenderApprovedOrOwner(approvedAddress, from, _msgSenderERC721A()))
            if (!isApprovedForAll(from, _msgSenderERC721A())) revert TransferCallerNotOwnerNorApproved();

        if (to == address(0)) revert TransferToZeroAddress();

        _beforeTokenTransfers(from, to, tokenId, 1);

        // Clear approvals from the previous owner.
        assembly {
            if approvedAddress {
                // This is equivalent to `delete _tokenApprovals[tokenId]`.
                sstore(approvedAddressSlot, 0)
            }
        }

        // Underflow of the sender's balance is impossible because we check for
        // ownership above and the recipient's balance can't realistically overflow.
        // Counter overflow is incredibly unrealistic as `tokenId` would have to be 2**256.
        unchecked {
            // We can directly increment and decrement the balances.
            --_packedAddressData[from]; // Updates: `balance -= 1`.
            ++_packedAddressData[to]; // Updates: `balance += 1`.

            // Updates:
            // - `address` to the next owner.
            // - `startTimestamp` to the timestamp of transfering.
            // - `burned` to `false`.
            // - `nextInitialized` to `true`.
            _packedOwnerships[tokenId] = _packOwnershipData(
                to,
                _BITMASK_NEXT_INITIALIZED | _nextExtraData(from, to, prevOwnershipPacked)
            );

            // If the next slot may not have been initialized (i.e. `nextInitialized == false`) .
            if (prevOwnershipPacked & _BITMASK_NEXT_INITIALIZED == 0) {
                uint256 nextTokenId = tokenId + 1;
                // If the next slot's address is zero and not burned (i.e. packed value is zero).
                if (_packedOwnerships[nextTokenId] == 0) {
                    // If the next slot is within bounds.
                    if (nextTokenId != _currentIndex) {
                        // Initialize the next slot to maintain correctness for `ownerOf(tokenId + 1)`.
                        _packedOwnerships[nextTokenId] = prevOwnershipPacked;
                    }
                }
            }
        }

        emit Transfer(from, to, tokenId);
        _afterTokenTransfers(from, to, tokenId, 1);
    }

    /**
     * @dev Equivalent to `safeTransferFrom(from, to, tokenId, '')`.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public payable virtual override {
        safeTransferFrom(from, to, tokenId, '');
    }

    /**
     * @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 memory _data
    ) public payable virtual override {
        transferFrom(from, to, tokenId);
        if (to.code.length != 0)
            if (!_checkContractOnERC721Received(from, to, tokenId, _data)) {
                revert TransferToNonERC721ReceiverImplementer();
            }
    }

    /**
     * @dev Hook that is called before a set of serially-ordered token IDs
     * are about to be transferred. This includes minting.
     * And also called before burning one token.
     *
     * `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`.
     * - When `to` is zero, `tokenId` will be burned by `from`.
     * - `from` and `to` are never both zero.
     */
    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.
     * And also called after one token has been burned.
     *
     * `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` has been
     * transferred to `to`.
     * - When `from` is zero, `tokenId` has been minted for `to`.
     * - When `to` is zero, `tokenId` has been burned by `from`.
     * - `from` and `to` are never both zero.
     */
    function _afterTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    ) internal virtual {}

    /**
     * @dev Private function to invoke {IERC721Receiver-onERC721Received} on a target contract.
     *
     * `from` - Previous owner of the given token ID.
     * `to` - Target address that will receive the token.
     * `tokenId` - Token ID to be transferred.
     * `_data` - Optional data to send along with the call.
     *
     * Returns whether the call correctly returned the expected magic value.
     */
    function _checkContractOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) private returns (bool) {
        try ERC721A__IERC721Receiver(to).onERC721Received(_msgSenderERC721A(), from, tokenId, _data) returns (
            bytes4 retval
        ) {
            return retval == ERC721A__IERC721Receiver(to).onERC721Received.selector;
        } catch (bytes memory reason) {
            if (reason.length == 0) {
                revert TransferToNonERC721ReceiverImplementer();
            } else {
                assembly {
                    revert(add(32, reason), mload(reason))
                }
            }
        }
    }

    // =============================================================
    //                        MINT OPERATIONS
    // =============================================================

    /**
     * @dev Mints `quantity` tokens and transfers them to `to`.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `quantity` must be greater than 0.
     *
     * Emits a {Transfer} event for each mint.
     */
    function _mint(address to, uint256 quantity) internal virtual {
        uint256 startTokenId = _currentIndex;
        if (quantity == 0) revert MintZeroQuantity();

        _beforeTokenTransfers(address(0), to, startTokenId, quantity);

        // Overflows are incredibly unrealistic.
        // `balance` and `numberMinted` have a maximum limit of 2**64.
        // `tokenId` has a maximum limit of 2**256.
        unchecked {
            // Updates:
            // - `balance += quantity`.
            // - `numberMinted += quantity`.
            //
            // We can directly add to the `balance` and `numberMinted`.
            _packedAddressData[to] += quantity * ((1 << _BITPOS_NUMBER_MINTED) | 1);

            // Updates:
            // - `address` to the owner.
            // - `startTimestamp` to the timestamp of minting.
            // - `burned` to `false`.
            // - `nextInitialized` to `quantity == 1`.
            _packedOwnerships[startTokenId] = _packOwnershipData(
                to,
                _nextInitializedFlag(quantity) | _nextExtraData(address(0), to, 0)
            );

            uint256 toMasked;
            uint256 end = startTokenId + quantity;

            // Use assembly to loop and emit the `Transfer` event for gas savings.
            // The duplicated `log4` removes an extra check and reduces stack juggling.
            // The assembly, together with the surrounding Solidity code, have been
            // delicately arranged to nudge the compiler into producing optimized opcodes.
            assembly {
                // Mask `to` to the lower 160 bits, in case the upper bits somehow aren't clean.
                toMasked := and(to, _BITMASK_ADDRESS)
                // Emit the `Transfer` event.
                log4(
                    0, // Start of data (0, since no data).
                    0, // End of data (0, since no data).
                    _TRANSFER_EVENT_SIGNATURE, // Signature.
                    0, // `address(0)`.
                    toMasked, // `to`.
                    startTokenId // `tokenId`.
                )

                // The `iszero(eq(,))` check ensures that large values of `quantity`
                // that overflows uint256 will make the loop run out of gas.
                // The compiler will optimize the `iszero` away for performance.
                for {
                    let tokenId := add(startTokenId, 1)
                } iszero(eq(tokenId, end)) {
                    tokenId := add(tokenId, 1)
                } {
                    // Emit the `Transfer` event. Similar to above.
                    log4(0, 0, _TRANSFER_EVENT_SIGNATURE, 0, toMasked, tokenId)
                }
            }
            if (toMasked == 0) revert MintToZeroAddress();

            _currentIndex = end;
        }
        _afterTokenTransfers(address(0), to, startTokenId, quantity);
    }

    /**
     * @dev Mints `quantity` tokens and transfers them to `to`.
     *
     * This function is intended for efficient minting only during contract creation.
     *
     * It emits only one {ConsecutiveTransfer} as defined in
     * [ERC2309](https://eips.ethereum.org/EIPS/eip-2309),
     * instead of a sequence of {Transfer} event(s).
     *
     * Calling this function outside of contract creation WILL make your contract
     * non-compliant with the ERC721 standard.
     * For full ERC721 compliance, substituting ERC721 {Transfer} event(s) with the ERC2309
     * {ConsecutiveTransfer} event is only permissible during contract creation.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `quantity` must be greater than 0.
     *
     * Emits a {ConsecutiveTransfer} event.
     */
    function _mintERC2309(address to, uint256 quantity) internal virtual {
        uint256 startTokenId = _currentIndex;
        if (to == address(0)) revert MintToZeroAddress();
        if (quantity == 0) revert MintZeroQuantity();
        if (quantity > _MAX_MINT_ERC2309_QUANTITY_LIMIT) revert MintERC2309QuantityExceedsLimit();

        _beforeTokenTransfers(address(0), to, startTokenId, quantity);

        // Overflows are unrealistic due to the above check for `quantity` to be below the limit.
        unchecked {
            // Updates:
            // - `balance += quantity`.
            // - `numberMinted += quantity`.
            //
            // We can directly add to the `balance` and `numberMinted`.
            _packedAddressData[to] += quantity * ((1 << _BITPOS_NUMBER_MINTED) | 1);

            // Updates:
            // - `address` to the owner.
            // - `startTimestamp` to the timestamp of minting.
            // - `burned` to `false`.
            // - `nextInitialized` to `quantity == 1`.
            _packedOwnerships[startTokenId] = _packOwnershipData(
                to,
                _nextInitializedFlag(quantity) | _nextExtraData(address(0), to, 0)
            );

            emit ConsecutiveTransfer(startTokenId, startTokenId + quantity - 1, address(0), to);

            _currentIndex = startTokenId + quantity;
        }
        _afterTokenTransfers(address(0), to, startTokenId, quantity);
    }

    /**
     * @dev Safely mints `quantity` tokens and transfers them to `to`.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement
     * {IERC721Receiver-onERC721Received}, which is called for each safe transfer.
     * - `quantity` must be greater than 0.
     *
     * See {_mint}.
     *
     * Emits a {Transfer} event for each mint.
     */
    function _safeMint(
        address to,
        uint256 quantity,
        bytes memory _data
    ) internal virtual {
        _mint(to, quantity);

        unchecked {
            if (to.code.length != 0) {
                uint256 end = _currentIndex;
                uint256 index = end - quantity;
                do {
                    if (!_checkContractOnERC721Received(address(0), to, index++, _data)) {
                        revert TransferToNonERC721ReceiverImplementer();
                    }
                } while (index < end);
                // Reentrancy protection.
                if (_currentIndex != end) revert();
            }
        }
    }

    /**
     * @dev Equivalent to `_safeMint(to, quantity, '')`.
     */
    function _safeMint(address to, uint256 quantity) internal virtual {
        _safeMint(to, quantity, '');
    }

    // =============================================================
    //                        BURN OPERATIONS
    // =============================================================

    /**
     * @dev Equivalent to `_burn(tokenId, false)`.
     */
    function _burn(uint256 tokenId) internal virtual {
        _burn(tokenId, false);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId, bool approvalCheck) internal virtual {
        uint256 prevOwnershipPacked = _packedOwnershipOf(tokenId);

        address from = address(uint160(prevOwnershipPacked));

        (uint256 approvedAddressSlot, address approvedAddress) = _getApprovedSlotAndAddress(tokenId);

        if (approvalCheck) {
            // The nested ifs save around 20+ gas over a compound boolean condition.
            if (!_isSenderApprovedOrOwner(approvedAddress, from, _msgSenderERC721A()))
                if (!isApprovedForAll(from, _msgSenderERC721A())) revert TransferCallerNotOwnerNorApproved();
        }

        _beforeTokenTransfers(from, address(0), tokenId, 1);

        // Clear approvals from the previous owner.
        assembly {
            if approvedAddress {
                // This is equivalent to `delete _tokenApprovals[tokenId]`.
                sstore(approvedAddressSlot, 0)
            }
        }

        // Underflow of the sender's balance is impossible because we check for
        // ownership above and the recipient's balance can't realistically overflow.
        // Counter overflow is incredibly unrealistic as `tokenId` would have to be 2**256.
        unchecked {
            // Updates:
            // - `balance -= 1`.
            // - `numberBurned += 1`.
            //
            // We can directly decrement the balance, and increment the number burned.
            // This is equivalent to `packed -= 1; packed += 1 << _BITPOS_NUMBER_BURNED;`.
            _packedAddressData[from] += (1 << _BITPOS_NUMBER_BURNED) - 1;

            // Updates:
            // - `address` to the last owner.
            // - `startTimestamp` to the timestamp of burning.
            // - `burned` to `true`.
            // - `nextInitialized` to `true`.
            _packedOwnerships[tokenId] = _packOwnershipData(
                from,
                (_BITMASK_BURNED | _BITMASK_NEXT_INITIALIZED) | _nextExtraData(from, address(0), prevOwnershipPacked)
            );

            // If the next slot may not have been initialized (i.e. `nextInitialized == false`) .
            if (prevOwnershipPacked & _BITMASK_NEXT_INITIALIZED == 0) {
                uint256 nextTokenId = tokenId + 1;
                // If the next slot's address is zero and not burned (i.e. packed value is zero).
                if (_packedOwnerships[nextTokenId] == 0) {
                    // If the next slot is within bounds.
                    if (nextTokenId != _currentIndex) {
                        // Initialize the next slot to maintain correctness for `ownerOf(tokenId + 1)`.
                        _packedOwnerships[nextTokenId] = prevOwnershipPacked;
                    }
                }
            }
        }

        emit Transfer(from, address(0), tokenId);
        _afterTokenTransfers(from, address(0), tokenId, 1);

        // Overflow not possible, as _burnCounter cannot be exceed _currentIndex times.
        unchecked {
            _burnCounter++;
        }
    }

    // =============================================================
    //                     EXTRA DATA OPERATIONS
    // =============================================================

    /**
     * @dev Directly sets the extra data for the ownership data `index`.
     */
    function _setExtraDataAt(uint256 index, uint24 extraData) internal virtual {
        uint256 packed = _packedOwnerships[index];
        if (packed == 0) revert OwnershipNotInitializedForExtraData();
        uint256 extraDataCasted;
        // Cast `extraData` with assembly to avoid redundant masking.
        assembly {
            extraDataCasted := extraData
        }
        packed = (packed & _BITMASK_EXTRA_DATA_COMPLEMENT) | (extraDataCasted << _BITPOS_EXTRA_DATA);
        _packedOwnerships[index] = packed;
    }

    /**
     * @dev Called during each token transfer to set the 24bit `extraData` field.
     * Intended to be overridden by the cosumer contract.
     *
     * `previousExtraData` - the value of `extraData` before transfer.
     *
     * 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, `tokenId` will be burned by `from`.
     * - `from` and `to` are never both zero.
     */
    function _extraData(
        address from,
        address to,
        uint24 previousExtraData
    ) internal view virtual returns (uint24) {}

    /**
     * @dev Returns the next extra data for the packed ownership data.
     * The returned result is shifted into position.
     */
    function _nextExtraData(
        address from,
        address to,
        uint256 prevOwnershipPacked
    ) private view returns (uint256) {
        uint24 extraData = uint24(prevOwnershipPacked >> _BITPOS_EXTRA_DATA);
        return uint256(_extraData(from, to, extraData)) << _BITPOS_EXTRA_DATA;
    }

    // =============================================================
    //                       OTHER OPERATIONS
    // =============================================================

    /**
     * @dev Returns the message sender (defaults to `msg.sender`).
     *
     * If you are writing GSN compatible contracts, you need to override this function.
     */
    function _msgSenderERC721A() internal view virtual returns (address) {
        return msg.sender;
    }

    /**
     * @dev Converts a uint256 to its ASCII string decimal representation.
     */
    function _toString(uint256 value) internal pure virtual returns (string memory str) {
        assembly {
            // The maximum value of a uint256 contains 78 digits (1 byte per digit), but
            // we allocate 0xa0 bytes to keep the free memory pointer 32-byte word aligned.
            // We will need 1 word for the trailing zeros padding, 1 word for the length,
            // and 3 words for a maximum of 78 digits. Total: 5 * 0x20 = 0xa0.
            let m := add(mload(0x40), 0xa0)
            // Update the free memory pointer to allocate.
            mstore(0x40, m)
            // Assign the `str` to the end.
            str := sub(m, 0x20)
            // Zeroize the slot after the string.
            mstore(str, 0)

            // Cache the end of the memory to calculate the length later.
            let end := str

            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            // prettier-ignore
            for { let temp := value } 1 {} {
                str := sub(str, 1)
                // Write the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(str, add(48, mod(temp, 10)))
                // Keep dividing `temp` until zero.
                temp := div(temp, 10)
                // prettier-ignore
                if iszero(temp) { break }
            }

            let length := sub(end, str)
            // Move the pointer 32 bytes leftwards to make room for the length.
            str := sub(str, 0x20)
            // Store the length.
            mstore(str, length)
        }
    }
}

// File: contracts/DateTime.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

// ----------------------------------------------------------------------------
// DateTime Library v2.0
//
// A gas-efficient Solidity date and time library
//
// https://github.com/bokkypoobah/BokkyPooBahsDateTimeLibrary
//
// Tested date range 1970/01/01 to 2345/12/31
//
// Conventions:
// Unit      | Range         | Notes
// :-------- |:-------------:|:-----
// timestamp | >= 0          | Unix timestamp, number of seconds since 1970/01/01 00:00:00 UTC
// year      | 1970 ... 2345 |
// month     | 1 ... 12      |
// day       | 1 ... 31      |
// hour      | 0 ... 23      |
// minute    | 0 ... 59      |
// second    | 0 ... 59      |
// dayOfWeek | 1 ... 7       | 1 = Monday, ..., 7 = Sunday
//
//
// Enjoy. (c) BokkyPooBah / Bok Consulting Pty Ltd 2018-2019. The MIT Licence.
// ----------------------------------------------------------------------------

library DateTime {
    uint256 constant SECONDS_PER_DAY = 24 * 60 * 60;
    uint256 constant SECONDS_PER_HOUR = 60 * 60;
    uint256 constant SECONDS_PER_MINUTE = 60;
    int256 constant OFFSET19700101 = 2440588;

    uint256 constant DOW_MON = 1;
    uint256 constant DOW_TUE = 2;
    uint256 constant DOW_WED = 3;
    uint256 constant DOW_THU = 4;
    uint256 constant DOW_FRI = 5;
    uint256 constant DOW_SAT = 6;
    uint256 constant DOW_SUN = 7;

    // ------------------------------------------------------------------------
    // Calculate the number of days from 1970/01/01 to year/month/day using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // and subtracting the offset 2440588 so that 1970/01/01 is day 0
    //
    // days = day
    //      - 32075
    //      + 1461 * (year + 4800 + (month - 14) / 12) / 4
    //      + 367 * (month - 2 - (month - 14) / 12 * 12) / 12
    //      - 3 * ((year + 4900 + (month - 14) / 12) / 100) / 4
    //      - offset
    // ------------------------------------------------------------------------
    function _daysFromDate(uint256 year, uint256 month, uint256 day) internal pure returns (uint256 _days) {
        require(year >= 1970);
        int256 _year = int256(year);
        int256 _month = int256(month);
        int256 _day = int256(day);

        int256 __days = _day - 32075 + (1461 * (_year + 4800 + (_month - 14) / 12)) / 4
            + (367 * (_month - 2 - ((_month - 14) / 12) * 12)) / 12
            - (3 * ((_year + 4900 + (_month - 14) / 12) / 100)) / 4 - OFFSET19700101;

        _days = uint256(__days);
    }

    // ------------------------------------------------------------------------
    // Calculate year/month/day from the number of days since 1970/01/01 using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // and adding the offset 2440588 so that 1970/01/01 is day 0
    //
    // int L = days + 68569 + offset
    // int N = 4 * L / 146097
    // L = L - (146097 * N + 3) / 4
    // year = 4000 * (L + 1) / 1461001
    // L = L - 1461 * year / 4 + 31
    // month = 80 * L / 2447
    // dd = L - 2447 * month / 80
    // L = month / 11
    // month = month + 2 - 12 * L
    // year = 100 * (N - 49) + year + L
    // ------------------------------------------------------------------------
    function _daysToDate(uint256 _days) internal pure returns (uint256 year, uint256 month, uint256 day) {
        unchecked {
            int256 __days = int256(_days);

            int256 L = __days + 68569 + OFFSET19700101;
            int256 N = (4 * L) / 146097;
            L = L - (146097 * N + 3) / 4;
            int256 _year = (4000 * (L + 1)) / 1461001;
            L = L - (1461 * _year) / 4 + 31;
            int256 _month = (80 * L) / 2447;
            int256 _day = L - (2447 * _month) / 80;
            L = _month / 11;
            _month = _month + 2 - 12 * L;
            _year = 100 * (N - 49) + _year + L;

            year = uint256(_year);
            month = uint256(_month);
            day = uint256(_day);
        }
    }

    function timestampFromDate(uint256 year, uint256 month, uint256 day) internal pure returns (uint256 timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY;
    }

    function timestampFromDateTime(
        uint256 year,
        uint256 month,
        uint256 day,
        uint256 hour,
        uint256 minute,
        uint256 second
    )
        internal
        pure
        returns (uint256 timestamp)
    {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + hour * SECONDS_PER_HOUR
            + minute * SECONDS_PER_MINUTE + second;
    }

    function timestampToDate(uint256 timestamp) internal pure returns (uint256 year, uint256 month, uint256 day) {
        unchecked {
            (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        }
    }

    function timestampToDateTime(uint256 timestamp)
        internal
        pure
        returns (uint256 year, uint256 month, uint256 day, uint256 hour, uint256 minute, uint256 second)
    {
        unchecked {
            (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
            uint256 secs = timestamp % SECONDS_PER_DAY;
            hour = secs / SECONDS_PER_HOUR;
            secs = secs % SECONDS_PER_HOUR;
            minute = secs / SECONDS_PER_MINUTE;
            second = secs % SECONDS_PER_MINUTE;
        }
    }

    function isValidDate(uint256 year, uint256 month, uint256 day) internal pure returns (bool valid) {
        if (year >= 1970 && month > 0 && month <= 12) {
            uint256 daysInMonth = _getDaysInMonth(year, month);
            if (day > 0 && day <= daysInMonth) {
                valid = true;
            }
        }
    }

    function isValidDateTime(uint256 year, uint256 month, uint256 day, uint256 hour, uint256 minute, uint256 second)
        internal
        pure
        returns (bool valid)
    {
        if (isValidDate(year, month, day)) {
            if (hour < 24 && minute < 60 && second < 60) {
                valid = true;
            }
        }
    }

    function isLeapYear(uint256 timestamp) internal pure returns (bool leapYear) {
        (uint256 year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        leapYear = _isLeapYear(year);
    }

    function _isLeapYear(uint256 year) internal pure returns (bool leapYear) {
        leapYear = ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
    }

    function isWeekDay(uint256 timestamp) internal pure returns (bool weekDay) {
        weekDay = getDayOfWeek(timestamp) <= DOW_FRI;
    }

    function isWeekEnd(uint256 timestamp) internal pure returns (bool weekEnd) {
        weekEnd = getDayOfWeek(timestamp) >= DOW_SAT;
    }

    function getDaysInMonth(uint256 timestamp) internal pure returns (uint256 daysInMonth) {
        (uint256 year, uint256 month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        daysInMonth = _getDaysInMonth(year, month);
    }

    function _getDaysInMonth(uint256 year, uint256 month) internal pure returns (uint256 daysInMonth) {
        if (month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
            daysInMonth = 31;
        } else if (month != 2) {
            daysInMonth = 30;
        } else {
            daysInMonth = _isLeapYear(year) ? 29 : 28;
        }
    }

    // 1 = Monday, 7 = Sunday
    function getDayOfWeek(uint256 timestamp) internal pure returns (uint256 dayOfWeek) {
        uint256 _days = timestamp / SECONDS_PER_DAY;
        dayOfWeek = ((_days + 3) % 7) + 1;
    }

    function getYear(uint256 timestamp) internal pure returns (uint256 year) {
        (year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }

    function getMonth(uint256 timestamp) internal pure returns (uint256 month) {
        (, month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }

    function getDay(uint256 timestamp) internal pure returns (uint256 day) {
        (,, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }

    function getHour(uint256 timestamp) internal pure returns (uint256 hour) {
        uint256 secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
    }

    function getMinute(uint256 timestamp) internal pure returns (uint256 minute) {
        uint256 secs = timestamp % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
    }

    function getSecond(uint256 timestamp) internal pure returns (uint256 second) {
        second = timestamp % SECONDS_PER_MINUTE;
    }

    function addYears(uint256 timestamp, uint256 _years) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year += _years;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + (timestamp % SECONDS_PER_DAY);
        require(newTimestamp >= timestamp);
    }

    function addMonths(uint256 timestamp, uint256 _months) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        month += _months;
        year += (month - 1) / 12;
        month = ((month - 1) % 12) + 1;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + (timestamp % SECONDS_PER_DAY);
        require(newTimestamp >= timestamp);
    }

    function addDays(uint256 timestamp, uint256 _days) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _days * SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }

    function addHours(uint256 timestamp, uint256 _hours) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _hours * SECONDS_PER_HOUR;
        require(newTimestamp >= timestamp);
    }

    function addMinutes(uint256 timestamp, uint256 _minutes) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp >= timestamp);
    }

    function addSeconds(uint256 timestamp, uint256 _seconds) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _seconds;
        require(newTimestamp >= timestamp);
    }

    function subYears(uint256 timestamp, uint256 _years) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year -= _years;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + (timestamp % SECONDS_PER_DAY);
        require(newTimestamp <= timestamp);
    }

    function subMonths(uint256 timestamp, uint256 _months) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint256 yearMonth = year * 12 + (month - 1) - _months;
        year = yearMonth / 12;
        month = (yearMonth % 12) + 1;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + (timestamp % SECONDS_PER_DAY);
        require(newTimestamp <= timestamp);
    }

    function subDays(uint256 timestamp, uint256 _days) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _days * SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }

    function subHours(uint256 timestamp, uint256 _hours) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _hours * SECONDS_PER_HOUR;
        require(newTimestamp <= timestamp);
    }

    function subMinutes(uint256 timestamp, uint256 _minutes) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp <= timestamp);
    }

    function subSeconds(uint256 timestamp, uint256 _seconds) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _seconds;
        require(newTimestamp <= timestamp);
    }

    function diffYears(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _years) {
        require(fromTimestamp <= toTimestamp);
        (uint256 fromYear,,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint256 toYear,,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _years = toYear - fromYear;
    }

    function diffMonths(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _months) {
        require(fromTimestamp <= toTimestamp);
        (uint256 fromYear, uint256 fromMonth,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint256 toYear, uint256 toMonth,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _months = toYear * 12 + toMonth - fromYear * 12 - fromMonth;
    }

    function diffDays(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _days) {
        require(fromTimestamp <= toTimestamp);
        _days = (toTimestamp - fromTimestamp) / SECONDS_PER_DAY;
    }

    function diffHours(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _hours) {
        require(fromTimestamp <= toTimestamp);
        _hours = (toTimestamp - fromTimestamp) / SECONDS_PER_HOUR;
    }

    function diffMinutes(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _minutes) {
        require(fromTimestamp <= toTimestamp);
        _minutes = (toTimestamp - fromTimestamp) / SECONDS_PER_MINUTE;
    }

    function diffSeconds(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _seconds) {
        require(fromTimestamp <= toTimestamp);
        _seconds = toTimestamp - fromTimestamp;
    }
}

// File: erc721a/contracts/IERC721A.sol



// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.2.3
// Creator: Chiru Labs

pragma solidity ^0.8.4;

/**
 * @dev Interface of ERC721A.
 */
interface IERC721A {
    /**
     * The caller must own the token or be an approved operator.
     */
    error ApprovalCallerNotOwnerNorApproved();

    /**
     * The token does not exist.
     */
    error ApprovalQueryForNonexistentToken();

    /**
     * Cannot query the balance for the zero address.
     */
    error BalanceQueryForZeroAddress();

    /**
     * Cannot mint to the zero address.
     */
    error MintToZeroAddress();

    /**
     * The quantity of tokens minted must be more than zero.
     */
    error MintZeroQuantity();

    /**
     * The token does not exist.
     */
    error OwnerQueryForNonexistentToken();

    /**
     * The caller must own the token or be an approved operator.
     */
    error TransferCallerNotOwnerNorApproved();

    /**
     * The token must be owned by `from`.
     */
    error TransferFromIncorrectOwner();

    /**
     * Cannot safely transfer to a contract that does not implement the
     * ERC721Receiver interface.
     */
    error TransferToNonERC721ReceiverImplementer();

    /**
     * Cannot transfer to the zero address.
     */
    error TransferToZeroAddress();

    /**
     * The token does not exist.
     */
    error URIQueryForNonexistentToken();

    /**
     * The `quantity` minted with ERC2309 exceeds the safety limit.
     */
    error MintERC2309QuantityExceedsLimit();

    /**
     * The `extraData` cannot be set on an unintialized ownership slot.
     */
    error OwnershipNotInitializedForExtraData();

    // =============================================================
    //                            STRUCTS
    // =============================================================

    struct TokenOwnership {
        // The address of the owner.
        address addr;
        // Stores the start time of ownership with minimal overhead for tokenomics.
        uint64 startTimestamp;
        // Whether the token has been burned.
        bool burned;
        // Arbitrary data similar to `startTimestamp` that can be set via {_extraData}.
        uint24 extraData;
    }

    // =============================================================
    //                         TOKEN COUNTERS
    // =============================================================

    /**
     * @dev Returns the total number of tokens in existence.
     * Burned tokens will reduce the count.
     * To get the total number of tokens minted, please see {_totalMinted}.
     */
    function totalSupply() external view returns (uint256);

    // =============================================================
    //                            IERC165
    // =============================================================

    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * [EIP section](https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified)
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);

    // =============================================================
    //                            IERC721
    // =============================================================

    /**
     * @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`,
     * 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 be 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,
        bytes calldata data
    ) external payable;

    /**
     * @dev Equivalent to `safeTransferFrom(from, to, tokenId, '')`.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external payable;

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {safeTransferFrom}
     * whenever possible.
     *
     * 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 payable;

    /**
     * @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 payable;

    /**
     * @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);

    // =============================================================
    //                        IERC721Metadata
    // =============================================================

    /**
     * @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);

    // =============================================================
    //                           IERC2309
    // =============================================================

    /**
     * @dev Emitted when tokens in `fromTokenId` to `toTokenId`
     * (inclusive) is transferred from `from` to `to`, as defined in the
     * [ERC2309](https://eips.ethereum.org/EIPS/eip-2309) standard.
     *
     * See {_mintERC2309} for more details.
     */
    event ConsecutiveTransfer(uint256 indexed fromTokenId, uint256 toTokenId, address indexed from, address indexed to);
}

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



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

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// File: @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;
    }
}