// Contract: DigiMiners
// Target function: function processProof(bytes32[] memory proof, bytes32 leaf)
Id,
    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)
    }
  }
}

library MerkleProof {
  /**
   * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
   * defined by `root`. For this, a `proof` must be provided, containing
   * sibling hashes on the branch from the leaf to the root of the tree. Each
   * pair of leaves and each pair of pre-images are assumed to be sorted.
   */
  function verify(
    bytes32[] memory proof,
    bytes32 root,
    bytes32 leaf
  ) internal pure returns (bool) {
    return processProof(proof, leaf) == root;
  }