contract ERC721A is Context, ERC165, IERC721, IERC721Metadata {
    using Address for address;
    using Strings for uint256;

    // Compiler will pack this into a single 256bit word.
    struct TokenOwnership {
        // The address of the owner.
        address addr;
        // Keeps track of the start time of ownership with minimal overhead for tokenomics.
        uint64 startTimestamp;
        // Whether the token has been burned.
        bool burned;
    }

    // Compiler will pack this into a single 256bit word.
    struct AddressData {
        // Realistically, 2**64-1 is more than enough.
        uint64 balance;
        // Keeps track of mint count with minimal overhead for tokenomics.
        uint64 numberMinted;
        // Keeps track of burn count with minimal overhead for tokenomics.
        uint64 numberBurned;
        // For storing miscellaneous variables.
        uint64 aux;
    }

    // The id of the next token to be minted.
    uint256 internal _currentIndex;

    // The number of tokens burned.
    uint256 internal _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 ownershipOf implementation for details.
    mapping(uint256 => TokenOwnership) internal _ownerships;

    // Mapping owner address to address data
    mapping(address => AddressData) private _addressData;

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

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

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

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

    /**
     * @dev See {IERC721Enumerable-totalSupply}.
     */
    function totalSupply() public view returns (uint256) {
        // Counter underflow is impossible as _burnCounter cannot be incremented
        // more than _currentIndex - _startTokenId() times
        unchecked {
            return _currentIndex - _burnCounter - _startTokenId();    
        }
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC721).interfaceId ||
            interfaceId == type(IERC721Metadata).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view override returns (uint256) {
        if (owner == address(0)) revert BalanceQueryForZeroAddress();
        return uint256(_addressData[owner].balance);
    }

    function _numberMinted(address owner) internal view returns (uint256) {
        if (owner == address(0)) revert MintedQueryForZeroAddress();
        return uint256(_addressData[owner].numberMinted);
    }

    function _numberBurned(address owner) internal view returns (uint256) {
        if (owner == address(0)) revert BurnedQueryForZeroAddress();
        return uint256(_addressData[owner].numberBurned);
    }

    function _getAux(address owner) internal view returns (uint64) {
        if (owner == address(0)) revert AuxQueryForZeroAddress();
        return _addressData[owner].aux;
    }

    function _setAux(address owner, uint64 aux) internal {
        if (owner == address(0)) revert AuxQueryForZeroAddress();
        _addressData[owner].aux = aux;
    }

    /**
     * Gas spent here starts off proportional to the maximum mint batch size.
     * It gradually moves to O(1) as tokens get transferred around in the collection over time.
     */
    function ownershipOf(uint256 tokenId) internal view returns (TokenOwnership memory) {
        uint256 curr = tokenId;

        unchecked {
            if (_startTokenId() <= curr && curr < _currentIndex) {
                TokenOwnership memory ownership = _ownerships[curr];
                if (!ownership.burned) {
                    if (ownership.addr != address(0)) {
                        return ownership;
                    }
                    // Invariant: 
                    // There will always be an ownership that has an address and is not burned 
                    // before an ownership that does not have an address and is not burned.
                    // Hence, curr will not underflow.
                    while (true) {
                        curr--;
                        ownership = _ownerships[curr];
                        if (ownership.addr != address(0)) {
                            return ownership;
                        }
                    }
                }
            }
        }
        revert OwnerQueryForNonexistentToken();
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view override returns (address) {
        return ownershipOf(tokenId).addr;
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
        if (!_exists(tokenId)) revert URIQueryForNonexistentToken();

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

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overriden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return '';
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public override {
        address owner = ERC721A.ownerOf(tokenId);
        if (to == owner) revert ApprovalToCurrentOwner();

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

        _approve(to, tokenId, owner);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId) public view override returns (address) {
        if (!_exists(tokenId)) revert ApprovalQueryForNonexistentToken();

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public override {
        if (operator == _msgSender()) revert ApproveToCaller();

        _operatorApprovals[_msgSender()][operator] = approved;
        emit ApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator) public view virtual override returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        safeTransferFrom(from, to, tokenId, '');
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) public virtual override {
        _transfer(from, to, tokenId);
        if (!_checkOnERC721Received(from, to, tokenId, _data)) {
            revert TransferToNonERC721ReceiverImplementer();
        }
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     */
    function _exists(uint256 tokenId) internal view returns (bool) {
        return _startTokenId() <= tokenId && tokenId < _currentIndex && 
            !_ownerships[tokenId].burned;
    }

    function _safeMint(address to, uint256 quantity) internal {
        _safeMint(to, 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.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(
        address to,
        uint256 quantity,
        bytes memory _data
    ) internal {
        _mint(to, quantity, _data, true);
    }

    /**
     * @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.
     */
    function _mint(
        address to,
        uint256 quantity,
        bytes memory _data,
        bool safe
    ) internal {
        uint256 startTokenId = _currentIndex;
        if (to == address(0)) revert MintToZeroAddress();
        if (quantity == 0) revert MintZeroQuantity();

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

        // Overflows are incredibly unrealistic.
        // balance or numberMinted overflow if current value of either + quantity > 1.8e19 (2**64 - 1)
        // updatedIndex overflows if _currentIndex + quantity > 1.2e77 (2**256 - 1)
        unchecked {
            _addressData[to].balance += uint64(quantity);
            _addressData[to].numberMinted += uint64(quantity);

            _ownerships[startTokenId].addr = to;
            _ownerships[startTokenId].startTimestamp = uint64(block.timestamp);

            uint256 updatedIndex = startTokenId;

            for (uint256 i; i < quantity; i++) {
                emit Transfer(address(0), to, updatedIndex);
                if (safe && !_checkOnERC721Received(address(0), to, updatedIndex, _data)) {
                    revert TransferToNonERC721ReceiverImplementer();
                }
                updatedIndex++;
            }

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

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) private {
        TokenOwnership memory prevOwnership = ownershipOf(tokenId);

        bool isApprovedOrOwner = (_msgSender() == prevOwnership.addr ||
            isApprovedForAll(prevOwnership.addr, _msgSender()) ||
            getApproved(tokenId) == _msgSender());

        if (!isApprovedOrOwner) revert TransferCallerNotOwnerNorApproved();
        if (prevOwnership.addr != from) revert TransferFromIncorrectOwner();
        if (to == address(0)) revert TransferToZeroAddress();

        _beforeTokenTransfers(from, to, tokenId, 1);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId, prevOwnership.addr);

        // 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 {
            _addressData[from].balance -= 1;
            _addressData[to].balance += 1;

            _ownerships[tokenId].addr = to;
            _ownerships[tokenId].startTimestamp = uint64(block.timestamp);

            // If the ownership slot of tokenId+1 is not explicitly set, that means the transfer initiator owns it.
            // Set the slot of tokenId+1 explicitly in storage to maintain correctness for ownerOf(tokenId+1) calls.
            uint256 nextTokenId = tokenId + 1;
            if (_ownerships[nextTokenId].addr == address(0)) {
                // This will suffice for checking _exists(nextTokenId),
                // as a burned slot cannot contain the zero address.
                if (nextTokenId < _currentIndex) {
                    _ownerships[nextTokenId].addr = prevOwnership.addr;
                    _ownerships[nextTokenId].startTimestamp = prevOwnership.startTimestamp;
                }
            }
        }

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

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

        _beforeTokenTransfers(prevOwnership.addr, address(0), tokenId, 1);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId, prevOwnership.addr);

        // 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 {
            _addressData[prevOwnership.addr].balance -= 1;
            _addressData[prevOwnership.addr].numberBurned += 1;

            // Keep track of who burned the token, and the timestamp of burning.
            _ownerships[tokenId].addr = prevOwnership.addr;
            _ownerships[tokenId].startTimestamp = uint64(block.timestamp);
            _ownerships[tokenId].burned = true;

            // If the ownership slot of tokenId+1 is not explicitly set, that means the burn initiator owns it.
            // Set the slot of tokenId+1 explicitly in storage to maintain correctness for ownerOf(tokenId+1) calls.
            uint256 nextTokenId = tokenId + 1;
            if (_ownerships[nextTokenId].addr == address(0)) {
                // This will suffice for checking _exists(nextTokenId),
                // as a burned slot cannot contain the zero address.
                if (nextTokenId < _currentIndex) {
                    _ownerships[nextTokenId].addr = prevOwnership.addr;
                    _ownerships[nextTokenId].startTimestamp = prevOwnership.startTimestamp;
                }
            }
        }

        emit Transfer(prevOwnership.addr, address(0), tokenId);
        _afterTokenTransfers(prevOwnership.addr, address(0), tokenId, 1);

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

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits a {Approval} event.
     */
    function _approve(
        address to,
        uint256 tokenId,
        address owner
    ) private {
        _tokenApprovals[tokenId] = to;
        emit Approval(owner, to, tokenId);
    }

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param _data bytes optional data to send along with the call
     * @return bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) private returns (bool) {
        if (to.isContract()) {
            try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, _data) returns (bytes4 retval) {
                return retval == IERC721Receiver(to).onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert TransferToNonERC721ReceiverImplementer();
                } else {
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before a set of serially-ordered token ids are about to be transferred. This includes minting.
     * 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 Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata extension. Built to optimize for lower gas during batch mints.
 *
 * Assumes serials are sequentially minted starting at _startTokenId() (defaults to 0, e.g. 0, 1, 2, 3..).
 *
 * Assumes that an owner cannot have more than 2**64 - 1 (max value of uint64) of supply.
 *
 * Assumes that the maximum token id cannot exceed 2**256 - 1 (max value of uint256).
 */
function _exists(uint256 tokenId) internal view returns (bool) {
    return _startTokenId() <= tokenId && tokenId < _currentIndex && 
        !_ownerships[tokenId].burned;
}

/**
 * @dev Returns whether `tokenId` exists.
 *
 * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
 *
 * Tokens start existing when they are minted (`_mint`),
 */