AEB BEGINS

/**
 *Submitted for verification at Etherscan.io on 2023-02-25
*/

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;


library Bytecode {
  error InvalidCodeAtRange(uint256 _size, uint256 _start, uint256 _end);

  /**
    @notice Generate a creation code that results on a contract with `_code` as bytecode
    @param _code The returning value of the resulting `creationCode`
    @return creationCode (constructor) for new contract
  */
  function creationCodeFor(bytes memory _code) internal pure returns (bytes memory) {
    /*
      0x00    0x63         0x63XXXXXX  PUSH4 _code.length  size
      0x01    0x80         0x80        DUP1                size size
      0x02    0x60         0x600e      PUSH1 14            14 size size
      0x03    0x60         0x6000      PUSH1 00            0 14 size size
      0x04    0x39         0x39        CODECOPY            size
      0x05    0x60         0x6000      PUSH1 00            0 size
      0x06    0xf3         0xf3        RETURN
      <CODE>
    */

    return abi.encodePacked(
      hex"63",
      uint32(_code.length),
      hex"80_60_0E_60_00_39_60_00_F3",
      _code
    );
  }

  /**
    @notice Returns the size of the code on a given address
    @param _addr Address that may or may not contain code
    @return size of the code on the given `_addr`
  */
  function codeSize(address _addr) internal view returns (uint256 size) {
    assembly { size := extcodesize(_addr) }
  }

  /**
    @notice Returns the code of a given address
    @dev It will fail if `_end < _start`
    @param _addr Address that may or may not contain code
    @param _start number of bytes of code to skip on read
    @param _end index before which to end extraction
    @return oCode read from `_addr` deployed bytecode

    Forked from: https://gist.github.com/KardanovIR/fe98661df9338c842b4a30306d507fbd
  */
  function codeAt(address _addr, uint256 _start, uint256 _end) internal view returns (bytes memory oCode) {
    uint256 csize = codeSize(_addr);
    if (csize == 0) return bytes("");

    if (_start > csize) return bytes("");
    if (_end < _start) revert InvalidCodeAtRange(csize, _start, _end); 

    unchecked {
      uint256 reqSize = _end - _start;
      uint256 maxSize = csize - _start;

      uint256 size = maxSize < reqSize ? maxSize : reqSize;

      assembly {
        // allocate output byte array - this could also be done without assembly
        // by using o_code = new bytes(size)
        oCode := mload(0x40)
        // new "memory end" including padding
        mstore(0x40, add(oCode, and(add(add(size, 0x20), 0x1f), not(0x1f))))
        // store length in memory
        mstore(oCode, size)
        // actually retrieve the code, this needs assembly
        extcodecopy(_addr, add(oCode, 0x20), _start, size)
      }
    }
  }
}
pragma solidity ^0.8.0;

/**
  @title A key-value storage with auto-generated keys for storing chunks of data with a lower write & read cost.
  @author Agustin Aguilar <aa@horizon.io>
  Readme: https://github.com/0xsequence/sstore2#readme
*/
library SSTORE2 {
  error WriteError();

  /**
    @notice Stores `_data` and returns `pointer` as key for later retrieval
    @dev The pointer is a contract address with `_data` as code
    @param _data to be written
    @return pointer Pointer to the written `_data`
  */
  function write(bytes memory _data) internal returns (address pointer) {
    // Append 00 to _data so contract can't be called
    // Build init code
    bytes memory code = Bytecode.creationCodeFor(
      abi.encodePacked(
        hex'00',
        _data
      )
    );

    // Deploy contract using create
    assembly { pointer := create(0, add(code, 32), mload(code)) }

    // Address MUST be non-zero
    if (pointer == address(0)) revert WriteError();
  }

  /**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte 
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @return data read from `_pointer` contract
  */
  function read(address _pointer) internal view returns (bytes memory) {
    return Bytecode.codeAt(_pointer, 1, type(uint256).max);
  }

  /**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte 
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @param _start number of bytes to skip
    @return data read from `_pointer` contract
  */
  function read(address _pointer, uint256 _start) internal view returns (bytes memory) {
    return Bytecode.codeAt(_pointer, _start + 1, type(uint256).max);
  }

  /**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte 
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @param _start number of bytes to skip
    @param _end index before which to end extraction
    @return data read from `_pointer` contract
  */
  function read(address _pointer, uint256 _start, uint256 _end) internal view returns (bytes memory) {
    return Bytecode.codeAt(_pointer, _start + 1, _end + 1);
  }
}

pragma solidity >=0.8.0 <0.9.0;


library BytesLib {
    function concat(
        bytes memory _preBytes,
        bytes memory _postBytes
    )
        internal
        pure
        returns (bytes memory)
    {
        bytes memory tempBytes;

        assembly {
            // Get a location of some free memory and store it in tempBytes as
            // Solidity does for memory variables.
            tempBytes := mload(0x40)

            // Store the length of the first bytes array at the beginning of
            // the memory for tempBytes.
            let length := mload(_preBytes)
            mstore(tempBytes, length)

            // Maintain a memory counter for the current write location in the
            // temp bytes array by adding the 32 bytes for the array length to
            // the starting location.
            let mc := add(tempBytes, 0x20)
            // Stop copying when the memory counter reaches the length of the
            // first bytes array.
            let end := add(mc, length)

            for {
                // Initialize a copy counter to the start of the _preBytes data,
                // 32 bytes into its memory.
                let cc := add(_preBytes, 0x20)
            } lt(mc, end) {
                // Increase both counters by 32 bytes each iteration.
                mc := add(mc, 0x20)
                cc := add(cc, 0x20)
            } {
                // Write the _preBytes data into the tempBytes memory 32 bytes
                // at a time.
                mstore(mc, mload(cc))
            }

            // Add the length of _postBytes to the current length of tempBytes
            // and store it as the new length in the first 32 bytes of the
            // tempBytes memory.
            length := mload(_postBytes)
            mstore(tempBytes, add(length, mload(tempBytes)))

            // Move the memory counter back from a multiple of 0x20 to the
            // actual end of the _preBytes data.
            mc := end
            // Stop copying when the memory counter reaches the new combined
            // length of the arrays.
            end := add(mc, length)

            for {
                let cc := add(_postBytes, 0x20)
            } lt(mc, end) {
                mc := add(mc, 0x20)
                cc := add(cc, 0x20)
            } {
                mstore(mc, mload(cc))
            }

            // Update the free-memory pointer by padding our last write location
            // to 32 bytes: add 31 bytes to the end of tempBytes to move to the
            // next 32 byte block, then round down to the nearest multiple of
            // 32. If the sum of the length of the two arrays is zero then add
            // one before rounding down to leave a blank 32 bytes (the length block with 0).
            mstore(0x40, and(
              add(add(end, iszero(add(length, mload(_preBytes)))), 31),
              not(31) // Round down to the nearest 32 bytes.
            ))
        }

        return tempBytes;
    }

    function concatStorage(bytes storage _preBytes, bytes memory _postBytes) internal {
        assembly {
            // Read the first 32 bytes of _preBytes storage, which is the length
            // of the array. (We don't need to use the offset into the slot
            // because arrays use the entire slot.)
            let fslot := sload(_preBytes.slot)
            // Arrays of 31 bytes or less have an even value in their slot,
            // while longer arrays have an odd value. The actual length is
            // the slot divided by two for odd values, and the lowest order
            // byte divided by two for even values.
            // If the slot is even, bitwise and the slot with 255 and divide by
            // two to get the length. If the slot is odd, bitwise and the slot
            // with -1 and divide by two.
            let slength := div(and(fslot, sub(mul(0x100, iszero(and(fslot, 1))), 1)), 2)
            let mlength := mload(_postBytes)
            let newlength := add(slength, mlength)
            // slength can contain both the length and contents of the array
            // if length < 32 bytes so let's prepare for that
            // v. http://solidity.readthedocs.io/en/latest/miscellaneous.html#layout-of-state-variables-in-storage
            switch add(lt(slength, 32), lt(newlength, 32))
            case 2 {
                // Since the new array still fits in the slot, we just need to
                // update the contents of the slot.
                // uint256(bytes_storage) = uint256(bytes_storage) + uint256(bytes_memory) + new_length
                sstore(
                    _preBytes.slot,
                    // all the modifications to the slot are inside this
                    // next block
                    add(
                        // we can just add to the slot contents because the
                        // bytes we want to change are the LSBs
                        fslot,
                        add(
                            mul(
                                div(
                                    // load the bytes from memory
                                    mload(add(_postBytes, 0x20)),
                                    // zero all bytes to the right
                                    exp(0x100, sub(32, mlength))
                                ),
                                // and now shift left the number of bytes to
                                // leave space for the length in the slot
                                exp(0x100, sub(32, newlength))
                            ),
                            // increase length by the double of the memory
                            // bytes length
                            mul(mlength, 2)
                        )
                    )
                )
            }
            case 1 {
                // The stored value fits in the slot, but the combined value
                // will exceed it.
                // get the keccak hash to get the contents of the array
                mstore(0x0, _preBytes.slot)
                let sc := add(keccak256(0x0, 0x20), div(slength, 32))

                // save new length
                sstore(_preBytes.slot, add(mul(newlength, 2), 1))

                // The contents of the _postBytes array start 32 bytes into
                // the structure. Our first read should obtain the `submod`
                // bytes that can fit into the unused space in the last word
                // of the stored array. To get this, we read 32 bytes starting
                // from `submod`, so the data we read overlaps with the array
                // contents by `submod` bytes. Masking the lowest-order
                // `submod` bytes allows us to add that value directly to the
                // stored value.

                let submod := sub(32, slength)
                let mc := add(_postBytes, submod)
                let end := add(_postBytes, mlength)
                let mask := sub(exp(0x100, submod), 1)

                sstore(
                    sc,
                    add(
                        and(
                            fslot,
                            0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00
                        ),
                        and(mload(mc), mask)
                    )
                )

                for {
                    mc := add(mc, 0x20)
                    sc := add(sc, 1)
                } lt(mc, end) {
                    sc := add(sc, 1)
                    mc := add(mc, 0x20)
                } {
                    sstore(sc, mload(mc))
                }

                mask := exp(0x100, sub(mc, end))

                sstore(sc, mul(div(mload(mc), mask), mask))
            }
            default {
                // get the keccak hash to get the contents of the array
                mstore(0x0, _preBytes.slot)
                // Start copying to the last used word of the stored array.
                let sc := add(keccak256(0x0, 0x20), div(slength, 32))

                // save new length
                sstore(_preBytes.slot, add(mul(newlength, 2), 1))

                // Copy over the first `submod` bytes of the new data as in
                // case 1 above.
                let slengthmod := mod(slength, 32)
                let mlengthmod := mod(mlength, 32)
                let submod := sub(32, slengthmod)
                let mc := add(_postBytes, submod)
                let end := add(_postBytes, mlength)
                let mask := sub(exp(0x100, submod), 1)

                sstore(sc, add(sload(sc), and(mload(mc), mask)))

                for {
                    sc := add(sc, 1)
                    mc := add(mc, 0x20)
                } lt(mc, end) {
                    sc := add(sc, 1)
                    mc := add(mc, 0x20)
                } {
                    sstore(sc, mload(mc))
                }

                mask := exp(0x100, sub(mc, end))

                sstore(sc, mul(div(mload(mc), mask), mask))
            }
        }
    }

    function slice(
        bytes memory _bytes,
        uint256 _start,
        uint256 _length
    )
        internal
        pure
        returns (bytes memory)
    {
        require(_length + 31 >= _length, "slice_overflow");
        require(_bytes.length >= _start + _length, "slice_outOfBounds");

        bytes memory tempBytes;

        assembly {
            switch iszero(_length)
            case 0 {
                // Get a location of some free memory and store it in tempBytes as
                // Solidity does for memory variables.
                tempBytes := mload(0x40)

                // The first word of the slice result is potentially a partial
                // word read from the original array. To read it, we calculate
                // the length of that partial word and start copying that many
                // bytes into the array. The first word we copy will start with
                // data we don't care about, but the last `lengthmod` bytes will
                // land at the beginning of the contents of the new array. When
                // we're done copying, we overwrite the full first word with
                // the actual length of the slice.
                let lengthmod := and(_length, 31)

                // The multiplication in the next line is necessary
                // because when slicing multiples of 32 bytes (lengthmod == 0)
                // the following copy loop was copying the origin's length
                // and then ending prematurely not copying everything it should.
                let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                let end := add(mc, _length)

                for {
                    // The multiplication in the next line has the same exact purpose
                    // as the one above.
                    let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                } lt(mc, end) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } {
                    mstore(mc, mload(cc))
                }

                mstore(tempBytes, _length)

                //update free-memory pointer
                //allocating the array padded to 32 bytes like the compiler does now
                mstore(0x40, and(add(mc, 31), not(31)))
            }
            //if we want a zero-length slice let's just return a zero-length array
            default {
                tempBytes := mload(0x40)
                //zero out the 32 bytes slice we are about to return
                //we need to do it because Solidity does not garbage collect
                mstore(tempBytes, 0)

                mstore(0x40, add(tempBytes, 0x20))
            }
        }

        return tempBytes;
    }

    function toAddress(bytes memory _bytes, uint256 _start) internal pure returns (address) {
        require(_bytes.length >= _start + 20, "toAddress_outOfBounds");
        address tempAddress;

        assembly {
            tempAddress := div(mload(add(add(_bytes, 0x20), _start)), 0x1000000000000000000000000)
        }

        return tempAddress;
    }

    function toUint8(bytes memory _bytes, uint256 _start) internal pure returns (uint8) {
        require(_bytes.length >= _start + 1 , "toUint8_outOfBounds");
        uint8 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x1), _start))
        }

        return tempUint;
    }

    function toUint16(bytes memory _bytes, uint256 _start) internal pure returns (uint16) {
        require(_bytes.length >= _start + 2, "toUint16_outOfBounds");
        uint16 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x2), _start))
        }

        return tempUint;
    }

    function toUint32(bytes memory _bytes, uint256 _start) internal pure returns (uint32) {
        require(_bytes.length >= _start + 4, "toUint32_outOfBounds");
        uint32 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x4), _start))
        }

        return tempUint;
    }

    function toUint64(bytes memory _bytes, uint256 _start) internal pure returns (uint64) {
        require(_bytes.length >= _start + 8, "toUint64_outOfBounds");
        uint64 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x8), _start))
        }

        return tempUint;
    }

    function toUint96(bytes memory _bytes, uint256 _start) internal pure returns (uint96) {
        require(_bytes.length >= _start + 12, "toUint96_outOfBounds");
        uint96 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0xc), _start))
        }

        return tempUint;
    }

    function toUint128(bytes memory _bytes, uint256 _start) internal pure returns (uint128) {
        require(_bytes.length >= _start + 16, "toUint128_outOfBounds");
        uint128 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x10), _start))
        }

        return tempUint;
    }

    function toUint256(bytes memory _bytes, uint256 _start) internal pure returns (uint256) {
        require(_bytes.length >= _start + 32, "toUint256_outOfBounds");
        uint256 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x20), _start))
        }

        return tempUint;
    }

    function toBytes32(bytes memory _bytes, uint256 _start) internal pure returns (bytes32) {
        require(_bytes.length >= _start + 32, "toBytes32_outOfBounds");
        bytes32 tempBytes32;

        assembly {
            tempBytes32 := mload(add(add(_bytes, 0x20), _start))
        }

        return tempBytes32;
    }

    function equal(bytes memory _preBytes, bytes memory _postBytes) internal pure returns (bool) {
        bool success = true;

        assembly {
            let length := mload(_preBytes)

            // if lengths don't match the arrays are not equal
            switch eq(length, mload(_postBytes))
            case 1 {
                // cb is a circuit breaker in the for loop since there's
                //  no said feature for inline assembly loops
                // cb = 1 - don't breaker
                // cb = 0 - break
                let cb := 1

                let mc := add(_preBytes, 0x20)
                let end := add(mc, length)

                for {
                    let cc := add(_postBytes, 0x20)
                // the next line is the loop condition:
                // while(uint256(mc < end) + cb == 2)
                } eq(add(lt(mc, end), cb), 2) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } {
                    // if any of these checks fails then arrays are not equal
                    if iszero(eq(mload(mc), mload(cc))) {
                        // unsuccess:
                        success := 0
                        cb := 0
                    }
                }
            }
            default {
                // unsuccess:
                success := 0
            }
        }

        return success;
    }

    function equalStorage(
        bytes storage _preBytes,
        bytes memory _postBytes
    )
        internal
        view
        returns (bool)
    {
        bool success = true;

        assembly {
            // we know _preBytes_offset is 0
            let fslot := sload(_preBytes.slot)
            // Decode the length of the stored array like in concatStorage().
            let slength := div(and(fslot, sub(mul(0x100, iszero(and(fslot, 1))), 1)), 2)
            let mlength := mload(_postBytes)

            // if lengths don't match the arrays are not equal
            switch eq(slength, mlength)
            case 1 {
                // slength can contain both the length and contents of the array
                // if length < 32 bytes so let's prepare for that
                // v. http://solidity.readthedocs.io/en/latest/miscellaneous.html#layout-of-state-variables-in-storage
                if iszero(iszero(slength)) {
                    switch lt(slength, 32)
                    case 1 {
                        // blank the last byte which is the length
                        fslot := mul(div(fslot, 0x100), 0x100)

                        if iszero(eq(fslot, mload(add(_postBytes, 0x20)))) {
                            // unsuccess:
                            success := 0
                        }
                    }
                    default {
                        // cb is a circuit breaker in the for loop since there's
                        //  no said feature for inline assembly loops
                        // cb = 1 - don't breaker
                        // cb = 0 - break
                        let cb := 1

                        // get the keccak hash to get the contents of the array
                        mstore(0x0, _preBytes.slot)
                        let sc := keccak256(0x0, 0x20)

                        let mc := add(_postBytes, 0x20)
                        let end := add(mc, mlength)

                        // the next line is the loop condition:
                        // while(uint256(mc < end) + cb == 2)
                        for {} eq(add(lt(mc, end), cb), 2) {
                            sc := add(sc, 1)
                            mc := add(mc, 0x20)
                        } {
                            if iszero(eq(sload(sc), mload(mc))) {
                                // unsuccess:
                                success := 0
                                cb := 0
                            }
                        }
                    }
                }
            }
            default {
                // unsuccess:
                success := 0
            }
        }

        return success;
    }
}



/**
 *Submitted for verification at Etherscan.io on 2023-02-17
*/

// File: @openzeppelin/contracts/utils/structs/EnumerableSet.sol


// OpenZeppelin Contracts (last updated v4.8.0) (utils/structs/EnumerableSet.sol)
// This file was procedurally generated from scripts/generate/templates/EnumerableSet.js.

pragma solidity ^0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 *
 * [WARNING]
 * ====
 * Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
 * unusable.
 * See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 * In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an
 * array of EnumerableSet.
 * ====
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            if (lastIndex != toDeleteIndex) {
                bytes32 lastValue = set._values[lastIndex];

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastValue;
                // Update the index for the moved value
                set._indexes[lastValue] = valueIndex; // Replace lastValue's index to valueIndex
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        bytes32[] memory store = _values(set._inner);
        bytes32[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }
}

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


// OpenZeppelin Contracts (last updated v4.7.0) (utils/StorageSlot.sol)

pragma solidity ^0.8.0;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
}

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


// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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


// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

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


// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;


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

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

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

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

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

// File: @openzeppelin/contracts/token/ERC721/IERC721Receiver.sol


// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.0;

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

// File: solidity-bits/contracts/Popcount.sol


/**
   _____       ___     ___ __           ____  _ __      
  / ___/____  / (_)___/ (_) /___  __   / __ )(_) /______
  \__ \/ __ \/ / / __  / / __/ / / /  / __  / / __/ ___/
 ___/ / /_/ / / / /_/ / / /_/ /_/ /  / /_/ / / /_(__  ) 
/____/\____/_/_/\__,_/_/\__/\__, /  /_____/_/\__/____/  
                           /____/                        

- npm: https://www.npmjs.com/package/solidity-bits
- github: https://github.com/estarriolvetch/solidity-bits

 */

pragma solidity ^0.8.0;

library Popcount {
    uint256 private constant m1 = 0x5555555555555555555555555555555555555555555555555555555555555555;
    uint256 private constant m2 = 0x3333333333333333333333333333333333333333333333333333333333333333;
    uint256 private constant m4 = 0x0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f;
    uint256 private constant h01 = 0x0101010101010101010101010101010101010101010101010101010101010101;

    function popcount256A(uint256 x) internal pure returns (uint256 count) {
        unchecked{
            for (count=0; x!=0; count++)
                x &= x - 1;
        }
    }

    function popcount256B(uint256 x) internal pure returns (uint256) {
        if (x == type(uint256).max) {
            return 256;
        }
        unchecked {
            x -= (x >> 1) & m1;             //put count of each 2 bits into those 2 bits
            x = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits 
            x = (x + (x >> 4)) & m4;        //put count of each 8 bits into those 8 bits 
            x = (x * h01) >> 248;  //returns left 8 bits of x + (x<<8) + (x<<16) + (x<<24) + ... 
        }
        return x;
    }
}
// File: solidity-bits/contracts/BitScan.sol


/**
   _____       ___     ___ __           ____  _ __      
  / ___/____  / (_)___/ (_) /___  __   / __ )(_) /______
  \__ \/ __ \/ / / __  / / __/ / / /  / __  / / __/ ___/
 ___/ / /_/ / / / /_/ / / /_/ /_/ /  / /_/ / / /_(__  ) 
/____/\____/_/_/\__,_/_/\__/\__, /  /_____/_/\__/____/  
                           /____/                        

- npm: https://www.npmjs.com/package/solidity-bits
- github: https://github.com/estarriolvetch/solidity-bits

 */

pragma solidity ^0.8.0;


library BitScan {
    uint256 constant private DEBRUIJN_256 = 0x818283848586878898a8b8c8d8e8f929395969799a9b9d9e9faaeb6bedeeff;
    bytes constant private LOOKUP_TABLE_256 = hex"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";

    /**
        @dev Isolate the least significant set bit.
     */ 
    function isolateLS1B256(uint256 bb) pure internal returns (uint256) {
        require(bb > 0);
        unchecked {
            return bb & (0 - bb);
        }
    } 

    /**
        @dev Isolate the most significant set bit.
     */ 
    function isolateMS1B256(uint256 bb) pure internal returns (uint256) {
        require(bb > 0);
        unchecked {
            bb |= bb >> 128;
            bb |= bb >> 64;
            bb |= bb >> 32;
            bb |= bb >> 16;
            bb |= bb >> 8;
            bb |= bb >> 4;
            bb |= bb >> 2;
            bb |= bb >> 1;
            
            return (bb >> 1) + 1;
        }
    } 

    /**
        @dev Find the index of the lest significant set bit. (trailing zero count)
     */ 
    function bitScanForward256(uint256 bb) pure internal returns (uint8) {
        unchecked {
            return uint8(LOOKUP_TABLE_256[(isolateLS1B256(bb) * DEBRUIJN_256) >> 248]);
        }   
    }

    /**
        @dev Find the index of the most significant set bit.
     */ 
    function bitScanReverse256(uint256 bb) pure internal returns (uint8) {
        unchecked {
            return 255 - uint8(LOOKUP_TABLE_256[((isolateMS1B256(bb) * DEBRUIJN_256) >> 248)]);
        }   
    }

    function log2(uint256 bb) pure internal returns (uint8) {
        unchecked {
            return uint8(LOOKUP_TABLE_256[(isolateMS1B256(bb) * DEBRUIJN_256) >> 248]);
        } 
    }
}

// File: solidity-bits/contracts/BitMaps.sol


/**
   _____       ___     ___ __           ____  _ __      
  / ___/____  / (_)___/ (_) /___  __   / __ )(_) /______
  \__ \/ __ \/ / / __  / / __/ / / /  / __  / / __/ ___/
 ___/ / /_/ / / / /_/ / / /_/ /_/ /  / /_/ / / /_(__  ) 
/____/\____/_/_/\__,_/_/\__/\__, /  /_____/_/\__/____/  
                           /____/                        

- npm: https://www.npmjs.com/package/solidity-bits
- github: https://github.com/estarriolvetch/solidity-bits

 */
pragma solidity ^0.8.0;



/**
 * @dev This Library is a modified version of Openzeppelin's BitMaps library with extra features.
 *
 * 1. Functions of finding the index of the closest set bit from a given index are added.
 *    The indexing of each bucket is modifed to count from the MSB to the LSB instead of from the LSB to the MSB.
 *    The modification of indexing makes finding the closest previous set bit more efficient in gas usage.
 * 2. Setting and unsetting the bitmap consecutively.
 * 3. Accounting number of set bits within a given range.   
 *
*/

/**
 * @dev Library for managing uint256 to bool mapping in a compact and efficient way, providing the keys are sequential.
 * Largelly inspired by Uniswap's https://github.com/Uniswap/merkle-distributor/blob/master/contracts/MerkleDistributor.sol[merkle-distributor].
 */

library BitMaps {
    using BitScan for uint256;
    uint256 private constant MASK_INDEX_ZERO = (1 << 255);
    uint256 private constant MASK_FULL = type(uint256).max;

    struct BitMap {
        mapping(uint256 => uint256) _data;
    }

    /**
     * @dev Returns whether the bit at `index` is set.
     */
    function get(BitMap storage bitmap, uint256 index) internal view returns (bool) {
        uint256 bucket = index >> 8;
        uint256 mask = MASK_INDEX_ZERO >> (index & 0xff);
        return bitmap._data[bucket] & mask != 0;
    }

    /**
     * @dev Sets the bit at `index` to the boolean `value`.
     */
    function setTo(
        BitMap storage bitmap,
        uint256 index,
        bool value
    ) internal {
        if (value) {
            set(bitmap, index);
        } else {
            unset(bitmap, index);
        }
    }

    /**
     * @dev Sets the bit at `index`.
     */
    function set(BitMap storage bitmap, uint256 index) internal {
        uint256 bucket = index >> 8;
        uint256 mask = MASK_INDEX_ZERO >> (index & 0xff);
        bitmap._data[bucket] |= mask;
    }

    /**
     * @dev Unsets the bit at `index`.
     */
    function unset(BitMap storage bitmap, uint256 index) internal {
        uint256 bucket = index >> 8;
        uint256 mask = MASK_INDEX_ZERO >> (index & 0xff);
        bitmap._data[bucket] &= ~mask;
    }


    /**
     * @dev Consecutively sets `amount` of bits starting from the bit at `startIndex`.
     */    
    function setBatch(BitMap storage bitmap, uint256 startIndex, uint256 amount) internal {
        uint256 bucket = startIndex >> 8;

        uint256 bucketStartIndex = (startIndex & 0xff);

        unchecked {
            if(bucketStartIndex + amount < 256) {
                bitmap._data[bucket] |= MASK_FULL << (256 - amount) >> bucketStartIndex;
            } else {
                bitmap._data[bucket] |= MASK_FULL >> bucketStartIndex;
                amount -= (256 - bucketStartIndex);
                bucket++;

                while(amount > 256) {
                    bitmap._data[bucket] = MASK_FULL;
                    amount -= 256;
                    bucket++;
                }

                bitmap._data[bucket] |= MASK_FULL << (256 - amount);
            }
        }
    }


    /**
     * @dev Consecutively unsets `amount` of bits starting from the bit at `startIndex`.
     */    
    function unsetBatch(BitMap storage bitmap, uint256 startIndex, uint256 amount) internal {
        uint256 bucket = startIndex >> 8;

        uint256 bucketStartIndex = (startIndex & 0xff);

        unchecked {
            if(bucketStartIndex + amount < 256) {
                bitmap._data[bucket] &= ~(MASK_FULL << (256 - amount) >> bucketStartIndex);
            } else {
                bitmap._data[bucket] &= ~(MASK_FULL >> bucketStartIndex);
                amount -= (256 - bucketStartIndex);
                bucket++;

                while(amount > 256) {
                    bitmap._data[bucket] = 0;
                    amount -= 256;
                    bucket++;
                }

                bitmap._data[bucket] &= ~(MASK_FULL << (256 - amount));
            }
        }
    }

    /**
     * @dev Returns number of set bits within a range.
     */
    function popcountA(BitMap storage bitmap, uint256 startIndex, uint256 amount) internal view returns(uint256 count) {
        uint256 bucket = startIndex >> 8;

        uint256 bucketStartIndex = (startIndex & 0xff);

        unchecked {
            if(bucketStartIndex + amount < 256) {
                count +=  Popcount.popcount256A(
                    bitmap._data[bucket] & (MASK_FULL << (256 - amount) >> bucketStartIndex)
                );
            } else {
                count += Popcount.popcount256A(
                    bitmap._data[bucket] & (MASK_FULL >> bucketStartIndex)
                );
                amount -= (256 - bucketStartIndex);
                bucket++;

                while(amount > 256) {
                    count += Popcount.popcount256A(bitmap._data[bucket]);
                    amount -= 256;
                    bucket++;
                }
                count += Popcount.popcount256A(
                    bitmap._data[bucket] & (MASK_FULL << (256 - amount))
                );
            }
        }
    }

    /**
     * @dev Returns number of set bits within a range.
     */
    function popcountB(BitMap storage bitmap, uint256 startIndex, uint256 amount) internal view returns(uint256 count) {
        uint256 bucket = startIndex >> 8;

        uint256 bucketStartIndex = (startIndex & 0xff);

        unchecked {
            if(bucketStartIndex + amount < 256) {
                count +=  Popcount.popcount256B(
                    bitmap._data[bucket] & (MASK_FULL << (256 - amount) >> bucketStartIndex)
                );
            } else {
                count += Popcount.popcount256B(
                    bitmap._data[bucket] & (MASK_FULL >> bucketStartIndex)
                );
                amount -= (256 - bucketStartIndex);
                bucket++;

                while(amount > 256) {
                    count += Popcount.popcount256B(bitmap._data[bucket]);
                    amount -= 256;
                    bucket++;
                }
                count += Popcount.popcount256B(
                    bitmap._data[bucket] & (MASK_FULL << (256 - amount))
                );
            }
        }
    }


    /**
     * @dev Find the closest index of the set bit before `index`.
     */
    function scanForward(BitMap storage bitmap, uint256 index) internal view returns (uint256 setBitIndex) {
        uint256 bucket = index >> 8;

        // index within the bucket
        uint256 bucketIndex = (index & 0xff);

        // load a bitboard from the bitmap.
        uint256 bb = bitmap._data[bucket];

        // offset the bitboard to scan from `bucketIndex`.
        bb = bb >> (0xff ^ bucketIndex); // bb >> (255 - bucketIndex)
        
        if(bb > 0) {
            unchecked {
                setBitIndex = (bucket << 8) | (bucketIndex -  bb.bitScanForward256());    
            }
        } else {
            while(true) {
                require(bucket > 0, "BitMaps: The set bit before the index doesn't exist.");
                unchecked {
                    bucket--;
                }
                // No offset. Always scan from the least significiant bit now.
                bb = bitmap._data[bucket];
                
                if(bb > 0) {
                    unchecked {
                        setBitIndex = (bucket << 8) | (255 -  bb.bitScanForward256());
                        break;
                    }
                } 
            }
        }
    }

    function getBucket(BitMap storage bitmap, uint256 bucket) internal view returns (uint256) {
        return bitmap._data[bucket];
    }
}

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


// OpenZeppelin Contracts (last updated v4.8.0) (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;
    }
}

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


// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

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

// File: @openzeppelin/contracts/token/ERC721/IERC721.sol


// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;


/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

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

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

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

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

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

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

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

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

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

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

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

// File: @openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol


// OpenZeppelin Contracts v4.4.1 (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.0;


/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

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

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

// File: @openzeppelin/contracts/utils/introspection/ERC165.sol


// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;


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

// File: @openzeppelin/contracts/interfaces/IERC2981.sol


// OpenZeppelin Contracts (last updated v4.6.0) (interfaces/IERC2981.sol)

pragma solidity ^0.8.0;


/**
 * @dev Interface for the NFT Royalty Standard.
 *
 * A standardized way to retrieve royalty payment information for non-fungible tokens (NFTs) to enable universal
 * support for royalty payments across all NFT marketplaces and ecosystem participants.
 *
 * _Available since v4.5._
 */
interface IERC2981 is IERC165 {
    /**
     * @dev Returns how much royalty is owed and to whom, based on a sale price that may be denominated in any unit of
     * exchange. The royalty amount is denominated and should be paid in that same unit of exchange.
     */
    function royaltyInfo(uint256 tokenId, uint256 salePrice)
        external
        view
        returns (address receiver, uint256 royaltyAmount);
}

// File: @openzeppelin/contracts/token/common/ERC2981.sol


// OpenZeppelin Contracts (last updated v4.7.0) (token/common/ERC2981.sol)

pragma solidity ^0.8.0;



/**
 * @dev Implementation of the NFT Royalty Standard, a standardized way to retrieve royalty payment information.
 *
 * Royalty information can be specified globally for all token ids via {_setDefaultRoyalty}, and/or individually for
 * specific token ids via {_setTokenRoyalty}. The latter takes precedence over the first.
 *
 * Royalty is specified as a fraction of sale price. {_feeDenominator} is overridable but defaults to 10000, meaning the
 * fee is specified in basis points by default.
 *
 * IMPORTANT: ERC-2981 only specifies a way to signal royalty information and does not enforce its payment. See
 * https://eips.ethereum.org/EIPS/eip-2981#optional-royalty-payments[Rationale] in the EIP. Marketplaces are expected to
 * voluntarily pay royalties together with sales, but note that this standard is not yet widely supported.
 *
 * _Available since v4.5._
 */
abstract contract ERC2981 is IERC2981, ERC165 {
    struct RoyaltyInfo {
        address receiver;
        uint96 royaltyFraction;
    }

    RoyaltyInfo private _defaultRoyaltyInfo;
    mapping(uint256 => RoyaltyInfo) private _tokenRoyaltyInfo;

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(IERC165, ERC165) returns (bool) {
        return interfaceId == type(IERC2981).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @inheritdoc IERC2981
     */
    function royaltyInfo(uint256 _tokenId, uint256 _salePrice) public view virtual override returns (address, uint256) {
        RoyaltyInfo memory royalty = _tokenRoyaltyInfo[_tokenId];

        if (royalty.receiver == address(0)) {
            royalty = _defaultRoyaltyInfo;
        }

        uint256 royaltyAmount = (_salePrice * royalty.royaltyFraction) / _feeDenominator();

        return (royalty.receiver, royaltyAmount);
    }

    /**
     * @dev The denominator with which to interpret the fee set in {_setTokenRoyalty} and {_setDefaultRoyalty} as a
     * fraction of the sale price. Defaults to 10000 so fees are expressed in basis points, but may be customized by an
     * override.
     */
    function _feeDenominator() internal pure virtual returns (uint96) {
        return 10000;
    }

    /**
     * @dev Sets the royalty information that all ids in this contract will default to.
     *
     * Requirements:
     *
     * - `receiver` cannot be the zero address.
     * - `feeNumerator` cannot be greater than the fee denominator.
     */
    function _setDefaultRoyalty(address receiver, uint96 feeNumerator) internal virtual {
        require(feeNumerator <= _feeDenominator(), "ERC2981: royalty fee will exceed salePrice");
        require(receiver != address(0), "ERC2981: invalid receiver");

        _defaultRoyaltyInfo = RoyaltyInfo(receiver, feeNumerator);
    }

    /**
     * @dev Removes default royalty information.
     */
    function _deleteDefaultRoyalty() internal virtual {
        delete _defaultRoyaltyInfo;
    }

    /**
     * @dev Sets the royalty information for a specific token id, overriding the global default.
     *
     * Requirements:
     *
     * - `receiver` cannot be the zero address.
     * - `feeNumerator` cannot be greater than the fee denominator.
     */
    function _setTokenRoyalty(
        uint256 tokenId,
        address receiver,
        uint96 feeNumerator
    ) internal virtual {
        require(feeNumerator <= _feeDenominator(), "ERC2981: royalty fee will exceed salePrice");
        require(receiver != address(0), "ERC2981: Invalid parameters");

        _tokenRoyaltyInfo[tokenId] = RoyaltyInfo(receiver, feeNumerator);
    }

    /**
     * @dev Resets royalty information for the token id back to the global default.
     */
    function _resetTokenRoyalty(uint256 tokenId) internal virtual {
        delete _tokenRoyaltyInfo[tokenId];
    }
}

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


// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

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

// File: erc721psi/contracts/ERC721Psi.sol


/**
  ______ _____   _____ ______ ___  __ _  _  _ 
 |  ____|  __ \ / ____|____  |__ \/_ | || || |
 | |__  | |__) | |        / /   ) || | \| |/ |
 |  __| |  _  /| |       / /   / / | |\_   _/ 
 | |____| | \ \| |____  / /   / /_ | |  | |   
 |______|_|  \_\\_____|/_/   |____||_|  |_|   

 - github: https://github.com/estarriolvetch/ERC721Psi
 - npm: https://www.npmjs.com/package/erc721psi
                                          
 */

pragma solidity ^0.8.0;

contract ERC721Psi is Context, ERC165, IERC721, IERC721Metadata {
    using Address for address;
    using Strings for uint256;
    using BitMaps for BitMaps.BitMap;

    BitMaps.BitMap internal _batchHead;

    string private _name;
    string private _symbol;

    // Mapping from token ID to owner address
    mapping(uint256 => address) internal _owners;
    uint256 internal _currentIndex;

    mapping(uint256 => address) private _tokenApprovals;
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
        _currentIndex = _startTokenId();
    }

    /**
     * @dev Returns the starting token ID.
     * To change the starting token ID, please override this function.
     */
    function _startTokenId() internal pure virtual returns (uint256) {
        // It will become modifiable in the future versions
        return 0;
    }

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

    /**
     * @dev Returns the total amount of tokens minted in the contract.
     */
    function _totalMinted() internal view virtual returns (uint256) {
        return _currentIndex - _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 
        virtual 
        override 
        returns (uint) 
    {
        require(owner != address(0), "ERC721Psi: balance query for the zero address");

        uint count;
        for( uint i = _startTokenId(); i < _nextTokenId(); ++i ){
            if(_exists(i)){
                if( owner == ownerOf(i)){
                    ++count;
                }
            }
        }
        return count;
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        (address owner, ) = _ownerAndBatchHeadOf(tokenId);
        return owner;
    }

    function _ownerAndBatchHeadOf(uint256 tokenId) internal view virtual returns (address owner, uint256 tokenIdBatchHead){
        require(_exists(tokenId), "ERC721Psi: owner query for nonexistent token");
        tokenIdBatchHead = _getBatchHead(tokenId);
        owner = _owners[tokenIdBatchHead];
    }

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

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

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
        require(_exists(tokenId), "ERC721Psi: URI query for nonexistent token");

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

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


    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ownerOf(tokenId);
        require(to != owner, "ERC721Psi: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721Psi: approve caller is not owner nor approved for all"
        );

        _approve(to, tokenId);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        require(
            _exists(tokenId),
            "ERC721Psi: approved query for nonexistent token"
        );

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved)
        public
        virtual
        override
    {
        require(operator != _msgSender(), "ERC721Psi: approve to caller");

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

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

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        //solhint-disable-next-line max-line-length
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721Psi: transfer caller is not owner nor approved"
        );

        _transfer(from, to, tokenId);
    }

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

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) public virtual override {
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721Psi: transfer caller is not owner nor approved"
        );
        _safeTransfer(from, to, tokenId, _data);
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * `_data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) internal virtual {
        _transfer(from, to, tokenId);
        require(
            _checkOnERC721Received(from, to, tokenId, 1,_data),
            "ERC721Psi: transfer to non ERC721Receiver implementer"
        );
    }

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

    /**
     * @dev Returns whether `spender` is allowed to manage `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId)
        internal
        view
        virtual
        returns (bool)
    {
        require(
            _exists(tokenId),
            "ERC721Psi: operator query for nonexistent token"
        );
        address owner = ownerOf(tokenId);
        return (spender == owner ||
            getApproved(tokenId) == spender ||
            isApprovedForAll(owner, spender));
    }

    /**
     * @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) internal virtual {
        _safeMint(to, quantity, "");
    }

    
    function _safeMint(
        address to,
        uint256 quantity,
        bytes memory _data
    ) internal virtual {
        uint256 nextTokenId = _nextTokenId();
        _mint(to, quantity);
        require(
            _checkOnERC721Received(address(0), to, nextTokenId, quantity, _data),
            "ERC721Psi: transfer to non ERC721Receiver implementer"
        );
    }


    function _mint(
        address to,
        uint256 quantity
    ) internal virtual {
        uint256 nextTokenId = _nextTokenId();
        
        require(quantity > 0, "ERC721Psi: quantity must be greater 0");
        require(to != address(0), "ERC721Psi: mint to the zero address");
        
        _beforeTokenTransfers(address(0), to, nextTokenId, quantity);
        _currentIndex += quantity;
        _owners[nextTokenId] = to;
        _batchHead.set(nextTokenId);
        _afterTokenTransfers(address(0), to, nextTokenId, quantity);
        
        // Emit events
        for(uint256 tokenId=nextTokenId; tokenId < nextTokenId + quantity; tokenId++){
            emit Transfer(address(0), to, tokenId);
        } 
    }



    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {
        (address owner, uint256 tokenIdBatchHead) = _ownerAndBatchHeadOf(tokenId);

        require(
            owner == from,
            "ERC721Psi: transfer of token that is not own"
        );
        require(to != address(0), "ERC721Psi: transfer to the zero address");

        _beforeTokenTransfers(from, to, tokenId, 1);

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

        uint256 subsequentTokenId = tokenId + 1;

        if(!_batchHead.get(subsequentTokenId) &&  
            subsequentTokenId < _nextTokenId()
        ) {
            _owners[subsequentTokenId] = from;
            _batchHead.set(subsequentTokenId);
        }

        _owners[tokenId] = to;
        if(tokenId != tokenIdBatchHead) {
            _batchHead.set(tokenId);
        }

        emit Transfer(from, to, tokenId);

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

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

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param startTokenId uint256 the first ID of the tokens to be transferred
     * @param quantity uint256 amount of the tokens to be transfered.
     * @param _data bytes optional data to send along with the call
     * @return r bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity,
        bytes memory _data
    ) private returns (bool r) {
        if (to.isContract()) {
            r = true;
            for(uint256 tokenId = startTokenId; tokenId < startTokenId + quantity; tokenId++){
                try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, _data) returns (bytes4 retval) {
                    r = r && retval == IERC721Receiver.onERC721Received.selector;
                } catch (bytes memory reason) {
                    if (reason.length == 0) {
                        revert("ERC721Psi: transfer to non ERC721Receiver implementer");
                    } else {
                        assembly {
                            revert(add(32, reason), mload(reason))
                        }
                    }
                }
            }
            return r;
        } else {
            return true;
        }
    }

    function _getBatchHead(uint256 tokenId) internal view returns (uint256 tokenIdBatchHead) {
        tokenIdBatchHead = _batchHead.scanForward(tokenId); 
    }


    function totalSupply() public virtual view returns (uint256) {
        return _totalMinted();
    }

    /**
     * @dev Returns an array of token IDs owned by `owner`.
     *
     * This function scans the ownership mapping and is O(`totalSupply`) in complexity.
     * It is meant to be called off-chain.
     *
     * This function is compatiable with ERC721AQueryable.
     */
    function tokensOfOwner(address owner) external view virtual returns (uint256[] memory) {
        unchecked {
            uint256 tokenIdsIdx;
            uint256 tokenIdsLength = balanceOf(owner);
            uint256[] memory tokenIds = new uint256[](tokenIdsLength);
            for (uint256 i = _startTokenId(); tokenIdsIdx != tokenIdsLength; ++i) {
                if (_exists(i)) {
                    if (ownerOf(i) == owner) {
                        tokenIds[tokenIdsIdx++] = i;
                    }
                }
            }
            return tokenIds;   
        }
    }

    /**
     * @dev Hook that is called before a set of serially-ordered token ids are about to be transferred. This includes minting.
     *
     * startTokenId - the first token id to be transferred
     * quantity - the amount to be transferred
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
     * transferred to `to`.
     * - When `from` is zero, `tokenId` will be minted for `to`.
     */
    function _beforeTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    ) internal virtual {}

    /**
     * @dev Hook that is called after a set of serially-ordered token ids have been transferred. This includes
     * minting.
     *
     * startTokenId - the first token id to be transferred
     * quantity - the amount to be transferred
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero.
     * - `from` and `to` are never both zero.
     */
    function _afterTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    ) internal virtual {}
}
// File: erc721psi/contracts/extension/ERC721PsiBurnable.sol


/**
  ______ _____   _____ ______ ___  __ _  _  _ 
 |  ____|  __ \ / ____|____  |__ \/_ | || || |
 | |__  | |__) | |        / /   ) || | \| |/ |
 |  __| |  _  /| |       / /   / / | |\_   _/ 
 | |____| | \ \| |____  / /   / /_ | |  | |   
 |______|_|  \_\\_____|/_/   |____||_|  |_|   
                                              
                                            
 */
pragma solidity ^0.8.0;




abstract contract ERC721PsiBurnable is ERC721Psi {
    using BitMaps for BitMaps.BitMap;
    BitMaps.BitMap internal _burnedToken;

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal virtual {
        address from = ownerOf(tokenId);
        _beforeTokenTransfers(from, address(0), tokenId, 1);
        _burnedToken.set(tokenId);
        
        emit Transfer(from, address(0), tokenId);

        _afterTokenTransfers(from, address(0), tokenId, 1);
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view override virtual returns (bool){
        if(_burnedToken.get(tokenId)) {
            return false;
        } 
        return super._exists(tokenId);
    }

    /**
     * @dev See {IERC721Enumerable-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalMinted() - _burned();
    }

    /**
     * @dev Returns number of token burned.
     */
    function _burned() internal view returns (uint256 burned){
        uint256 startBucket = _startTokenId() >> 8;
        uint256 lastBucket = (_nextTokenId() >> 8) + 1;

        for(uint256 i=startBucket; i < lastBucket; i++) {
            uint256 bucket = _burnedToken.getBucket(i);
            burned += _popcount(bucket);
        }
    }

    /**
     * @dev Returns number of set bits.
     */
    function _popcount(uint256 x) private pure returns (uint256 count) {
        unchecked{
            for (count=0; x!=0; count++)
                x &= x - 1;
        }
    }
}
// File: @openzeppelin/contracts/access/Ownable.sol


// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;


/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

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

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

// File: EXO/NEW/EXO.sol

pragma solidity >=0.6.0;

/// @title Base64
/// @author Brecht Devos - <brecht@loopring.org>
/// @notice Provides functions for encoding/decoding base64
library Base64 {
    string internal constant TABLE_ENCODE = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/';
    bytes  internal constant TABLE_DECODE = hex"0000000000000000000000000000000000000000000000000000000000000000"
                                            hex"00000000000000000000003e0000003f3435363738393a3b3c3d000000000000"
                                            hex"00000102030405060708090a0b0c0d0e0f101112131415161718190000000000"
                                            hex"001a1b1c1d1e1f202122232425262728292a2b2c2d2e2f303132330000000000";

    function encode(bytes memory data) internal pure returns (string memory) {
        if (data.length == 0) return '';

        // load the table into memory
        string memory table = TABLE_ENCODE;

        // multiply by 4/3 rounded up
        uint256 encodedLen = 4 * ((data.length + 2) / 3);

        // add some extra buffer at the end required for the writing
        string memory result = new string(encodedLen + 32);

        assembly {
            // set the actual output length
            mstore(result, encodedLen)

            // prepare the lookup table
            let tablePtr := add(table, 1)

            // input ptr
            let dataPtr := data
            let endPtr := add(dataPtr, mload(data))

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

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

                // write 4 characters
                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1)
                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1)
                mstore8(resultPtr, mload(add(tablePtr, and(shr( 6, input), 0x3F))))
                resultPtr := add(resultPtr, 1)
                mstore8(resultPtr, mload(add(tablePtr, and(        input,  0x3F))))
                resultPtr := add(resultPtr, 1)
            }

            // padding with '='
            switch mod(mload(data), 3)
            case 1 { mstore(sub(resultPtr, 2), shl(240, 0x3d3d)) }
            case 2 { mstore(sub(resultPtr, 1), shl(248, 0x3d)) }
        }

        return result;
    }

    function decode(string memory _data) internal pure returns (bytes memory) {
        bytes memory data = bytes(_data);

        if (data.length == 0) return new bytes(0);
        require(data.length % 4 == 0, "invalid base64 decoder input");

        // load the table into memory
        bytes memory table = TABLE_DECODE;

        // every 4 characters represent 3 bytes
        uint256 decodedLen = (data.length / 4) * 3;

        // add some extra buffer at the end required for the writing
        bytes memory result = new bytes(decodedLen + 32);

        assembly {
            // padding with '='
            let lastBytes := mload(add(data, mload(data)))
            if eq(and(lastBytes, 0xFF), 0x3d) {
                decodedLen := sub(decodedLen, 1)
                if eq(and(lastBytes, 0xFFFF), 0x3d3d) {
                    decodedLen := sub(decodedLen, 1)
                }
            }

            // set the actual output length
            mstore(result, decodedLen)

            // prepare the lookup table
            let tablePtr := add(table, 1)

            // input ptr
            let dataPtr := data
            let endPtr := add(dataPtr, mload(data))

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

            // run over the input, 4 characters at a time
            for {} lt(dataPtr, endPtr) {}
            {
               // read 4 characters
               dataPtr := add(dataPtr, 4)
               let input := mload(dataPtr)

               // write 3 bytes
               let output := add(
                   add(
                       shl(18, and(mload(add(tablePtr, and(shr(24, input), 0xFF))), 0xFF)),
                       shl(12, and(mload(add(tablePtr, and(shr(16, input), 0xFF))), 0xFF))),
                   add(
                       shl( 6, and(mload(add(tablePtr, and(shr( 8, input), 0xFF))), 0xFF)),
                               and(mload(add(tablePtr, and(        input , 0xFF))), 0xFF)
                    )
                )
                mstore(resultPtr, shl(232, output))
                resultPtr := add(resultPtr, 3)
            }
        }

        return result;
    }
}






pragma solidity ^0.8.7;


abstract contract MerkleProof {
    mapping(uint256 => bytes32) internal _wlMerkleRoot;
    mapping(uint256 => bytes32) internal _alMerkleRoot;

    uint256 public phaseId;
    function _setWlMerkleRoot(bytes32 merkleRoot_) internal virtual {
        _wlMerkleRoot[phaseId] = merkleRoot_;
    }

    function _setWlMerkleRootWithId(uint256 _phaseId,bytes32 merkleRoot_) internal virtual {
        _wlMerkleRoot[_phaseId] = merkleRoot_;
    }
    function isWhitelisted(address address_, uint256 _phaseId, uint256 wlCount, bytes32[] memory proof_) public view returns (bool) {
        bytes32 _leaf = keccak256(abi.encodePacked(address_, wlCount));
        for (uint256 i = 0; i < proof_.length; i++) {
            _leaf = _leaf < proof_[i] ? keccak256(abi.encodePacked(_leaf, proof_[i])) : keccak256(abi.encodePacked(proof_[i], _leaf));
        }
        return _leaf == _wlMerkleRoot[_phaseId];
    }

    function _setAlMerkleRootWithId(uint256 _phaseId,bytes32 merkleRoot_) internal virtual {
        _alMerkleRoot[_phaseId] = merkleRoot_;
    }

    function _setAlMerkleRoot(bytes32 merkleRoot_) internal virtual {
        _alMerkleRoot[phaseId] = merkleRoot_;
    }

    function isAllowlisted(address address_,uint256 _alId, bytes32[] memory proof_) public view returns (bool) {
        bytes32 _leaf = keccak256(abi.encodePacked(address_));
        for (uint256 i = 0; i < proof_.length; i++) {
            _leaf = _leaf < proof_[i] ? keccak256(abi.encodePacked(_leaf, proof_[i])) : keccak256(abi.encodePacked(proof_[i], _leaf));
        }
        return _leaf == _alMerkleRoot[_alId];
    }

}

pragma solidity ^0.8.9;
abstract contract Operable is Context {
    mapping(address => bool) _operators;
    modifier onlyOperator() {
        _checkOperatorRole(_msgSender());
        _;
    }
    function isOperator(address _operator) public view returns (bool) {
        return _operators[_operator];
    }
    function _grantOperatorRole(address _candidate) internal {
        require(
            !_operators[_candidate],
            string(
                abi.encodePacked(
                    "account ",
                    Strings.toHexString(uint160(_msgSender()), 20),
                    " is already has an operator role"
                )
            )
        );
        _operators[_candidate] = true;
    }
    function _revokeOperatorRole(address _candidate) internal {
        _checkOperatorRole(_candidate);
        delete _operators[_candidate];
    }
    function _checkOperatorRole(address _operator) internal view {
        require(
            _operators[_operator],
            string(
                abi.encodePacked(
                    "account ",
                    Strings.toHexString(uint160(_msgSender()), 20),
                    " is not an operator"
                )
            )
        );
    }
}

pragma solidity ^0.8.13;

interface IOperatorFilterRegistry {
    function isOperatorAllowed(address registrant, address operator) external view returns (bool);
    function register(address registrant) external;
    function registerAndSubscribe(address registrant, address subscription) external;
    function registerAndCopyEntries(address registrant, address registrantToCopy) external;
    function unregister(address addr) external;
    function updateOperator(address registrant, address operator, bool filtered) external;
    function updateOperators(address registrant, address[] calldata operators, bool filtered) external;
    function updateCodeHash(address registrant, bytes32 codehash, bool filtered) external;
    function updateCodeHashes(address registrant, bytes32[] calldata codeHashes, bool filtered) external;
    function subscribe(address registrant, address registrantToSubscribe) external;
    function unsubscribe(address registrant, bool copyExistingEntries) external;
    function subscriptionOf(address addr) external returns (address registrant);
    function subscribers(address registrant) external returns (address[] memory);
    function subscriberAt(address registrant, uint256 index) external returns (address);
    function copyEntriesOf(address registrant, address registrantToCopy) external;
    function isOperatorFiltered(address registrant, address operator) external returns (bool);
    function isCodeHashOfFiltered(address registrant, address operatorWithCode) external returns (bool);
    function isCodeHashFiltered(address registrant, bytes32 codeHash) external returns (bool);
    function filteredOperators(address addr) external returns (address[] memory);
    function filteredCodeHashes(address addr) external returns (bytes32[] memory);
    function filteredOperatorAt(address registrant, uint256 index) external returns (address);
    function filteredCodeHashAt(address registrant, uint256 index) external returns (bytes32);
    function isRegistered(address addr) external returns (bool);
    function codeHashOf(address addr) external returns (bytes32);
}

pragma solidity ^0.8.13;


/**
 * @title  OperatorFilterer
 * @notice Abstract contract whose constructor automatically registers and optionally subscribes to or copies another
 *         registrant's entries in the OperatorFilterRegistry.
 * @dev    This smart contract is meant to be inherited by token contracts so they can use the following:
 *         - `onlyAllowedOperator` modifier for `transferFrom` and `safeTransferFrom` methods.
 *         - `onlyAllowedOperatorApproval` modifier for `approve` and `setApprovalForAll` methods.
 */
abstract contract OperatorFilterer {
    error OperatorNotAllowed(address operator);
    bool public operatorFilteringEnabled = true;

    IOperatorFilterRegistry public constant OPERATOR_FILTER_REGISTRY =
        IOperatorFilterRegistry(0x000000000000AAeB6D7670E522A718067333cd4E);

    constructor(address subscriptionOrRegistrantToCopy, bool subscribe) {
        // If an inheriting token contract is deployed to a network without the registry deployed, the modifier
        // will not revert, but the contract will need to be registered with the registry once it is deployed in
        // order for the modifier to filter addresses.
        if (address(OPERATOR_FILTER_REGISTRY).code.length > 0) {
            if (subscribe) {
                OPERATOR_FILTER_REGISTRY.registerAndSubscribe(address(this), subscriptionOrRegistrantToCopy);
            } else {
                if (subscriptionOrRegistrantToCopy != address(0)) {
                    OPERATOR_FILTER_REGISTRY.registerAndCopyEntries(address(this), subscriptionOrRegistrantToCopy);
                } else {
                    OPERATOR_FILTER_REGISTRY.register(address(this));
                }
            }
        }
    }

    modifier onlyAllowedOperator(address from) virtual {
        // Check registry code length to facilitate testing in environments without a deployed registry.
        if (address(OPERATOR_FILTER_REGISTRY).code.length > 0 && operatorFilteringEnabled) {
            // Allow spending tokens from addresses with balance
            // Note that this still allows listings and marketplaces with escrow to transfer tokens if transferred
            // from an EOA.
            if (from == msg.sender) {
                _;
                return;
            }
            if (!OPERATOR_FILTER_REGISTRY.isOperatorAllowed(address(this), msg.sender)) {
                revert OperatorNotAllowed(msg.sender);
            }
        }
        _;
    }

    modifier onlyAllowedOperatorApproval(address operator) virtual {
        // Check registry code length to facilitate testing in environments without a deployed registry.
        if (address(OPERATOR_FILTER_REGISTRY).code.length > 0 && operatorFilteringEnabled) {
            if (!OPERATOR_FILTER_REGISTRY.isOperatorAllowed(address(this), operator)) {
                revert OperatorNotAllowed(operator);
            }
        }
        _;
    }
}


pragma solidity ^0.8.13;
/**
 * @title  DefaultOperatorFilterer
 * @notice Inherits from OperatorFilterer and automatically subscribes to the default OpenSea subscription.
 */
abstract contract DefaultOperatorFilterer is OperatorFilterer {
    address constant DEFAULT_SUBSCRIPTION = address(0x3cc6CddA760b79bAfa08dF41ECFA224f810dCeB6);

    constructor() OperatorFilterer(DEFAULT_SUBSCRIPTION, true) {}
}





pragma solidity >=0.7.0 <0.9.0;

interface IContractAllowListProxy {
    function isAllowed(address _transferer, uint256 _level)
        external
        view
        returns (bool);
}

pragma solidity >=0.8.0;

/// @title IERC721RestrictApprove
/// @dev Approve抑制機能付きコントラクトのインターフェース
/// @author Lavulite

interface IERC721RestrictApprove {
    /**
     * @dev CALレベルが変更された場合のイベント
     */
    event CalLevelChanged(address indexed operator, uint256 indexed level);
    
    /**
     * @dev LocalContractAllowListnに追加された場合のイベント
     */
    event LocalCalAdded(address indexed operator, address indexed transferer);

    /**
     * @dev LocalContractAllowListnに削除された場合のイベント
     */
    event LocalCalRemoved(address indexed operator, address indexed transferer);

    /**
     * @dev CALを利用する場合のCALのレベルを設定する。レベルが高いほど、許可されるコントラクトの範囲が狭い。
     */
    function setCALLevel(uint256 level) external;

    /**
     * @dev CALのアドレスをセットする。
     */
    function setCAL(address calAddress) external;

    /**
     * @dev CALのリストに無い独自の許可アドレスを追加する場合、こちらにアドレスを記載する。
     */
    function addLocalContractAllowList(address transferer) external;

    /**
     * @dev CALのリストにある独自の許可アドレスを削除する場合、こちらにアドレスを記載する。
     */
    function removeLocalContractAllowList(address transferer) external;

    /**
     * @dev CALのリストにある独自の許可アドレスの一覧を取得する。
     */
    function getLocalContractAllowList() external view returns(address[] memory);

}

pragma solidity >=0.8.0;

/// @title AntiScam機能付きERC721A
/// @dev Readmeを見てください。

abstract contract ERC721RestrictApprove is ERC721PsiBurnable, IERC721RestrictApprove {
    using EnumerableSet for EnumerableSet.AddressSet;

    IContractAllowListProxy public CAL;
    EnumerableSet.AddressSet localAllowedAddresses;

    modifier onlyHolder(uint256 tokenId) {
        require(
            msg.sender == ownerOf(tokenId),
            "RestrictApprove: operation is only holder."
        );
        _;
    }

    /*//////////////////////////////////////////////////////////////
    変数
    //////////////////////////////////////////////////////////////*/
    bool public enableRestrict = true;

    // token lock
    mapping(uint256 => uint256) public tokenCALLevel;

    // wallet lock
    mapping(address => uint256) public walletCALLevel;

    // contract lock
    uint256 public CALLevel = 1;

    /*///////////////////////////////////////////////////////////////
    Approve抑制機能ロジック
    //////////////////////////////////////////////////////////////*/
    function _addLocalContractAllowList(address transferer)
        internal
        virtual
    {
        localAllowedAddresses.add(transferer);
        emit LocalCalAdded(msg.sender, transferer);
    }

    function _removeLocalContractAllowList(address transferer)
        internal
        virtual
    {
        localAllowedAddresses.remove(transferer);
        emit LocalCalRemoved(msg.sender, transferer);
    }

    function _getLocalContractAllowList()
        internal
        virtual
        view
        returns(address[] memory)
    {
        return localAllowedAddresses.values();
    }

    function _isLocalAllowed(address transferer)
        internal
        view
        virtual
        returns (bool)
    {
        return localAllowedAddresses.contains(transferer);
    }

    function _isAllowed(address transferer)
        internal
        view
        virtual
        returns (bool)
    {
        return _isAllowed(msg.sender, transferer);
    }

    function _isAllowed(uint256 tokenId, address transferer)
        internal
        view
        virtual
        returns (bool)
    {
        uint256 level = _getCALLevel(msg.sender, tokenId);
        return _isAllowed(transferer, level);
    }

    function _isAllowed(address holder, address transferer)
        internal
        view
        virtual
        returns (bool)
    {
        uint256 level = _getCALLevel(holder);
        return _isAllowed(transferer, level);
    }

    function _isAllowed(address transferer, uint256 level)
        internal
        view
        virtual
        returns (bool)
    {
        if (!enableRestrict) {
            return true;
        }

        return _isLocalAllowed(transferer) || CAL.isAllowed(transferer, level);
    }

    function _getCALLevel(address holder, uint256 tokenId)
        internal
        view
        virtual
        returns (uint256)
    {
        if (tokenCALLevel[tokenId] > 0) {
            return tokenCALLevel[tokenId];
        }

        return _getCALLevel(holder);
    }

    function _getCALLevel(address holder)
        internal
        view
        virtual
        returns (uint256)
    {
        if (walletCALLevel[holder] > 0) {
            return walletCALLevel[holder];
        }

        return CALLevel;
    }

    function _setCAL(address _cal) internal virtual {
        CAL = IContractAllowListProxy(_cal);
    }

    function _deleteTokenCALLevel(uint256 tokenId) internal virtual {
        delete tokenCALLevel[tokenId];
    }

    function setTokenCALLevel(uint256 tokenId, uint256 level)
        external
        virtual
        onlyHolder(tokenId)
    {
        tokenCALLevel[tokenId] = level;
    }

    function setWalletCALLevel(uint256 level)
        external
        virtual
    {
        walletCALLevel[msg.sender] = level;
    }

    /*///////////////////////////////////////////////////////////////
                              OVERRIDES
    //////////////////////////////////////////////////////////////*/

    function isApprovedForAll(address owner, address operator)
        public
        view
        virtual
        override
        returns (bool)
    {
        if (_isAllowed(owner, operator) == false) {
            return false;
        }
        return super.isApprovedForAll(owner, operator);
    }

    function setApprovalForAll(address operator, bool approved)
        public
        virtual
        override
    {
        require(
            _isAllowed(operator) || approved == false,
            "RestrictApprove: Can not approve locked token"
        );
        super.setApprovalForAll(operator, approved);
    }

    function _beforeApprove(address to, uint256 tokenId)
        internal
        virtual
    {
        if (to != address(0)) {
            require(_isAllowed(tokenId, to), "RestrictApprove: The contract is not allowed.");
        }
    }

    function approve(address to, uint256 tokenId)
        public
        virtual
        override
    {
        _beforeApprove(to, tokenId);
        super.approve(to, tokenId);
    }

    function _afterTokenTransfers(
        address from,
        address, /*to*/
        uint256 startTokenId,
        uint256 /*quantity*/
    ) internal virtual override {
        // 転送やバーンにおいては、常にstartTokenIdは TokenIDそのものとなります。
        if (from != address(0)) {
            // CALレベルをデフォルトに戻す。
            _deleteTokenCALLevel(startTokenId);
        }
    }

    function supportsInterface(bytes4 interfaceId)
        public
        view
        virtual
        override
        returns (bool)
    {
        return
            interfaceId == type(IERC721RestrictApprove).interfaceId ||
            super.supportsInterface(interfaceId);
    }
}


pragma solidity ^0.8.7;
/*
╭━━━┳━━━┳━━╮╱╭━━╮╭━━━┳━━━┳━━┳━╮╱╭┳━━━╮
┃╭━╮┃╭━━┫╭╮┃╱┃╭╮┃┃╭━━┫╭━╮┣┫┣┫┃╰╮┃┃╭━╮┃
┃┃╱┃┃╰━━┫╰╯╰╮┃╰╯╰┫╰━━┫┃╱╰╯┃┃┃╭╮╰╯┃╰━━╮
┃╰━╯┃╭━━┫╭━╮┃┃╭━╮┃╭━━┫┃╭━╮┃┃┃┃╰╮┃┣━━╮┃
┃╭━╮┃╰━━┫╰━╯┃┃╰━╯┃╰━━┫╰┻━┣┫┣┫┃╱┃┃┃╰━╯┃
╰╯╱╰┻━━━┻━━━╯╰━━━┻━━━┻━━━┻━━┻╯╱╰━┻━━━╯
*/
contract AEBBEGINS is Ownable, ERC721RestrictApprove, ReentrancyGuard, MerkleProof, ERC2981, DefaultOperatorFilterer,Operable {
  //Project Settings
  mapping(uint256 => uint256) public alMintPrice;
  uint256 public psMintPrice = 0.05 ether;
  uint256 public wlMintPrice;  
  mapping(uint256 => uint256) public maxMintsPerAL;
  uint256 public maxMintsPerPS = 2;
  uint256 public maxMintsPerALOT = 30;
  uint256 public maxMintsPerPSOT = 2;
  uint256 public maxSupply;
  uint256 public mintable;
  uint256 public revealed;
  uint256 public nowPhaseWl;
  uint256 public nowPhaseAl;
  uint256 public nowPhasePs;

  address internal _withdrawWallet;
  address internal _aa;
  address internal _bb;
  address internal _cc;
  address internal _dd;
  address internal _ee;
  address internal _ff;

  uint256 internal _aaPerc;
  uint256 internal _bbPerc;
  uint256 internal _ccPerc;
  uint256 internal _ddPerc;
  uint256 internal _eePerc;
  uint256 internal _ffPerc;

  //URI
  string internal hiddenURI;
  string internal _baseTokenURI;
  string public _baseExtension = ".json";

  //flags
  mapping(uint256 => bool) public isWlSaleEnabled;
  mapping(uint256 => bool) public isAlSaleEnabled;
  bool public isPublicSaleEnabled;
  bool internal lockBurn = true;

  //mint records.
  mapping(uint256 => uint256) public phaseIds;
  mapping(uint256 => mapping(address => uint256)) internal _wlMinted;
  mapping(uint256 => mapping(uint256 => mapping(address => uint256))) internal _alMinted;
  mapping(uint256 => mapping(address => uint256)) internal _psMinted;
  
  constructor (
    address _royaltyReceiver,
    uint96 _royaltyFraction,
    uint256 _aaPercAdd
  ) ERC721Psi ("AEB BEGINS","AEB") {
    _grantOperatorRole(msg.sender);
    _grantOperatorRole(_royaltyReceiver);
    _setDefaultRoyalty(_royaltyReceiver,_royaltyFraction);
    //CAL initialization
    setCALLevel(1);
    _setCAL(0xF2A78c73ffBAB6ECc3548Acc54B546ace279312E);//Ethereum mainnet proxy
    _addLocalContractAllowList(0x1E0049783F008A0085193E00003D00cd54003c71);//OpenSea
    _addLocalContractAllowList(0x4feE7B061C97C9c496b01DbcE9CDb10c02f0a0Be);//Rarible
    maxMintsPerAL[0] = 10;//fcfs
    maxMintsPerAL[1] = 30;//VVIP1
    maxMintsPerAL[2] = 20;//VVIP2
    maxMintsPerAL[3] = 20;//VIP1
    maxMintsPerAL[4] = 20;//VIP2
    maxMintsPerAL[5] = 10;//VIP3
    maxMintsPerAL[6] = 10;//VIP4
    maxMintsPerAL[7] = 10;//kaku

    alMintPrice[0] = 0.05 ether;//fcfs
    alMintPrice[1] = 0.02 ether;//VVIP1
    alMintPrice[2] = 0.03 ether;//VVIP2
    alMintPrice[3] = 0.025 ether;//VIP1
    alMintPrice[4] = 0.035 ether;//VIP2
    alMintPrice[5] = 0.04 ether;//VIP3
    alMintPrice[6] = 0.045 ether;//VIP4
    alMintPrice[7] = 0.05 ether;//k
    
    hiddenURI = "https://arweave.net/QQCSg9F1i63yAUu7NRLT5ncvDE3HCrqFxpl6K8iboh4";
    _aa = msg.sender;
    _aaPerc = _aaPercAdd;
  }
  //start from 1.adjust.
  function _startTokenId() internal pure virtual override returns (uint256) {
        return 1;
  }
  //set Default Royalty._feeNumerator 500 = 5% Royalty
  function setDefaultRoyalty(address _receiver, uint96 _feeNumerator) external virtual onlyOperator {
      _setDefaultRoyalty(_receiver, _feeNumerator);
  }
  //for ERC2981
  function supportsInterface(bytes4 interfaceId) public view virtual override(ERC721RestrictApprove, ERC2981) returns (bool) {
    return super.supportsInterface(interfaceId);
  }
  //for ERC2981 Opensea
  function contractURI() external view virtual returns (string memory) {
        return _formatContractURI();
  }
  //make contractURI
  function _formatContractURI() internal view returns (string memory) {
    (address receiver, uint256 royaltyFraction) = royaltyInfo(0,_feeDenominator());//tokenid=0
    return string(
      abi.encodePacked(
        "data:application/json;base64,",
        Base64.encode(
          bytes(
            abi.encodePacked(
                '{"seller_fee_basis_points":', Strings.toString(royaltyFraction),
                ', "fee_recipient":"', Strings.toHexString(uint256(uint160(receiver)), 20), '"}'
            )
          )
        )
      )
    );
  }
  //set maxSupply.only owner.
  function setMaxSupply(uint256 _maxSupply) external virtual onlyOperator {
    maxSupply = _maxSupply;
  }
  //set mintable.only owner.
  function setMintable(uint256 _mintable) external virtual onlyOperator {
    mintable = _mintable;
  }
    // GET phaseId.
  function getPhaseIds(uint256 _alId) external view virtual returns (uint256){
    return phaseIds[_alId];
  }
    // SET phaseId.
  function setPhaseId(uint256 _alId,uint256 _phaseId) external virtual onlyOperator {
    phaseIds[_alId] = _phaseId;
  }
    // SET phaseId.
  function setPhaseIdWithReset(uint256 _alId,uint256 _phaseId) external virtual onlyOperator {
    phaseIds[_alId] = _phaseId;
    nowPhaseAl += 1;
  }
  function setNowPhaseWl(uint256 _nowPhaseWl) external virtual onlyOperator {
    nowPhaseWl = _nowPhaseWl;
  }
  function setNowPhaseAl(uint256 _nowPhaseAl) external virtual onlyOperator {
    nowPhaseAl = _nowPhaseAl;
  }
  function setNowPhasePs(uint256 _nowPhasePs) external virtual onlyOperator {
    nowPhasePs = _nowPhasePs;
  }
  // SET PRICES.
  //WL.Price
  function setWlPrice(uint256 newPrice) external virtual onlyOperator {
    wlMintPrice = newPrice;
  }
  //AL.Price
  function setAlPrice(uint256 _alId,uint256 newPrice) external virtual onlyOperator {
    alMintPrice[_alId] = newPrice;
  }
  //PS.Price
  function setPsPrice(uint256 newPrice) external virtual onlyOperator {
    psMintPrice = newPrice;
  }
  //set reveal.only owner.
  function setReveal(uint256 newRevealNum) external virtual onlyOperator {
    revealed = newRevealNum;
  }
  //return _isRevealed()
  function _isRevealed(uint256 _tokenId) internal view virtual returns (bool){
    return _tokenId <= revealed;
  }
  // GET MINTED COUNT.
  function wlMinted(address _address) external view virtual returns (uint256){
    return _wlMinted[nowPhaseWl][_address];
  }
  function alMinted(address _address) external view virtual returns (uint256){
    return _alMinted[nowPhaseAl][phaseIds[nowPhaseAl]][_address];
  }
  function alIdMinted(uint256 _nowPhaseAl,address _address) external view virtual returns (uint256){
    return _alMinted[_nowPhaseAl][phaseIds[_nowPhaseAl]][_address];
  }
  function psMinted(address _address) external view virtual returns (uint256){
    return _psMinted[nowPhasePs][_address];
  }
  // SET MAX MINTS.
  //get.AL.mxmints
  function getAlMaxMints() external view virtual returns (uint256){
    return maxMintsPerAL[phaseId];
  }
  //set.AL.mxmints
  function setAlMaxMints(uint256 _alId,uint256 _max) external virtual onlyOperator {
    maxMintsPerAL[_alId] = _max;
  }
  //PS.mxmints
  function setPsMaxMints(uint256 _max) external virtual onlyOperator {
    maxMintsPerPS = _max;
  }
  // SET SALES ENABLE.
  //WL.SaleEnable
  function setWhitelistSaleEnable(uint256 _phaseId,bool bool_) external virtual onlyOperator {
    isWlSaleEnabled[_phaseId] = bool_;
  }

  //AL.SaleEnable
  function setAllowlistSaleEnable(uint256 _alId,bool bool_) external virtual onlyOperator {
    isAlSaleEnabled[_alId] = bool_;
  }
  //PS.SaleEnable
  function setPublicSaleEnable(bool bool_) external virtual onlyOperator {
    isPublicSaleEnabled = bool_;
  }

  function setMerkleRootWl(bytes32 merkleRoot_) external virtual onlyOperator {
    _setWlMerkleRoot(merkleRoot_);
  }

  function setMerkleRootWlWithId(uint256 _phaseId,bytes32 merkleRoot_) external virtual onlyOperator {
    _setWlMerkleRootWithId(_phaseId,merkleRoot_);
  }

  function setMerkleRootAlWithId(uint256 _phaseId,bytes32 merkleRoot_) external virtual onlyOperator {
    _setAlMerkleRootWithId(_phaseId,merkleRoot_);
  }
  //set HiddenBaseURI.only owner.
  function setHiddenURI(string memory uri_) external virtual onlyOperator {
    hiddenURI = uri_;
  }
  //return _currentIndex
  function getCurrentIndex() external view virtual returns (uint256){
    return _nextTokenId() -1;
  }
  /** @dev set BaseURI at after reveal. only owner. */
  function setBaseURI(string memory uri_) external virtual onlyOperator {
    _baseTokenURI = uri_;
  }

  function setBaseExtension(string memory _newBaseExtension) external onlyOperator
  {
    _baseExtension = _newBaseExtension;
  }

  /** @dev BaseURI.internal. */
  function _currentBaseURI() internal view returns (string memory){
    return _baseTokenURI;
  }

  function tokenURI(uint256 _tokenId) public view virtual override returns (string memory) {
    require(_exists(_tokenId), "URI query for nonexistent token");
    if(_isRevealed(_tokenId)){
        return string(abi.encodePacked(_currentBaseURI(), Strings.toString(_tokenId), _baseExtension));
    }
    return hiddenURI;
  }
  
  /** @dev owner mint.transfer to _address.only owner. */
  function ownerMintSafe(uint256 _amount, address _address) external virtual onlyOperator { 
    require((_amount + totalSupply()) <= (maxSupply) || maxSupply == 0, "No more NFTs");
    _safeMint(_address, _amount);
  }
  
  //WL mint.
  function whitelistMint(uint256 _phaseId,uint256 _amount, uint256 wlcount, bytes32[] memory proof_) external payable virtual nonReentrant {
    require(isWlSaleEnabled[_phaseId], "whitelistMint is Paused");
    require(isWhitelisted(msg.sender,_phaseId, wlcount, proof_), "You are not whitelisted!");
    require(wlcount > 0, "You have no WL!");
    require(wlcount >= _amount, "whitelistMint: Over max mints per wallet");
    require(wlcount >= _wlMinted[_phaseId][msg.sender] + _amount, "You have no whitelistMint left");
    require(msg.value == wlMintPrice * _amount, "ETH value is not correct");
    require((_amount + totalSupply()) <= (mintable) || mintable == 0, "No more NFTs");
    _wlMinted[_phaseId][msg.sender] += _amount;
    _safeMint(msg.sender, _amount);
  }
  
  //AL mint.
  function allowlistMint(uint256 _alId,uint256 _amount, bytes32[] memory proof_) external payable virtual nonReentrant {
    require(isAlSaleEnabled[_alId], "allowlistMint is Paused");
    require(isAllowlisted(msg.sender,_alId, proof_), "You are not whitelisted!");
    require(maxMintsPerALOT >= _amount, "allowlistMint: Over max mints per one time");
    require(maxMintsPerAL[_alId] >= _amount, "allowlistMint: Over max mints per wallet");
    require(maxMintsPerAL[_alId] >= _alMinted[_alId][phaseIds[_alId]][msg.sender] + _amount, "You have no whitelistMint left");
    require(msg.value == alMintPrice[_alId] * _amount, "ETH value is not correct");
    require((_amount + totalSupply()) <= (mintable) || mintable == 0, "No more NFTs");
    _alMinted[_alId][phaseIds[_alId]][msg.sender] += _amount;
    _safeMint(msg.sender, _amount);
  }

  //Public mint.
  function publicMint(uint256 _amount) external payable virtual nonReentrant {
    require(isPublicSaleEnabled, "publicMint is Paused");
    require(maxMintsPerPSOT >= _amount, "publicMint: Over max mints per one time");
    require(maxMintsPerPS >= _amount, "publicMint: Over max mints per wallet");
    require(maxMintsPerPS >= _psMinted[nowPhasePs][msg.sender] + _amount, "You have no publicMint left");
    require(msg.value == psMintPrice * _amount, "ETH value is not correct");
    require((_amount + totalSupply()) <= (mintable) || mintable == 0, "No more NFTs");
    _psMinted[nowPhasePs][msg.sender] += _amount;
    _safeMint(msg.sender, _amount);
  }

  /** @dev receive. */
  function receiveToDeb() external payable virtual onlyOperator nonReentrant {
      require(msg.value > 0, "ETH value is not correct");
  }

  /** @dev widraw ETH from this contract.only operator. */
  function withdraw() external payable virtual onlyOperator nonReentrant{
    require((_aa != address(0) && _aaPerc != 0) || _aa == address(0),"please set withdraw Address_aa and percentage.");
    require((_bb != address(0) && _bbPerc != 0) || _bb == address(0),"please set withdraw Address_bb and percentage.");
    require((_cc != address(0) && _ccPerc != 0) || _cc == address(0),"please set withdraw Address_cc and percentage.");
    require((_dd != address(0) && _ddPerc != 0) || _dd == address(0),"please set withdraw Address_dd and percentage.");
    require((_ee != address(0) && _eePerc != 0) || _ee == address(0),"please set withdraw Address_ee and percentage.");
    require((_ff != address(0) && _ffPerc != 0) || _ff == address(0),"please set withdraw Address_ff and percentage.");
    uint256 _ethBalance = address(this).balance;
    bool os;
    if(_aa != address(0)){//if _aa has.
        (os, ) = payable(_aa).call{value: (_ethBalance * _aaPerc/10000)}("");
        require(os, "Failed to withdraw_aa Ether");
    }
    if(_bb != address(0)){//if _bb has.
        (os, ) = payable(_bb).call{value: (_ethBalance * _bbPerc/10000)}("");
        require(os, "Failed to withdraw_bb Ether");
    }
    if(_cc != address(0)){//if _cc has.
        (os, ) = payable(_cc).call{value: (_ethBalance * _ccPerc/10000)}("");
        require(os, "Failed to withdraw_cc Ether");
    }
    if(_dd != address(0)){//if _dd has.
        (os, ) = payable(_dd).call{value: (_ethBalance * _ddPerc/10000)}("");
        require(os, "Failed to withdraw_dd Ether");
    }
    if(_ee != address(0)){//if _ee has.
        (os, ) = payable(_ee).call{value: (_ethBalance * _eePerc/10000)}("");
        require(os, "Failed to withdraw_ee Ether");
    }
    if(_ff != address(0)){//if _ff has.
        (os, ) = payable(_ff).call{value: (_ethBalance * _ffPerc/10000)}("");
        require(os, "Failed to withdraw_ff Ether");
    }
    _ethBalance = address(this).balance;
    if(_withdrawWallet != address(0)){//if _withdrawWallet has.
        (os, ) = payable(_withdrawWallet).call{value: (_ethBalance)}("");
    }else{
        (os, ) = payable(owner()).call{value: (_ethBalance)}("");
    }
    require(os, "Failed to withdraw Ether");
  }

    //burn
    function burn(uint256 tokenId) external virtual {
        require(ownerOf(tokenId) == msg.sender, "isnt owner token");
        require(lockBurn == false, "not allow");
        _burn(tokenId);
    }
    // //set.LockBurn
    function setLockBurn(bool bool_) external virtual onlyOperator {
        lockBurn = bool_;
    }

  //return wallet owned tokenids.
  function walletOfOwner(address _address) external view virtual returns (uint256[] memory) {
    uint256 ownerTokenCount = balanceOf(_address);
    uint256[] memory tokenIds = new uint256[](ownerTokenCount);
    //search from all tonkenid. so spend high gas values.attention.
    uint256 tokenindex = 0;
    for (uint256 i = _startTokenId(); i < (_nextTokenId() -1); i++) {
      if(_address == this.tryOwnerOf(i)) tokenIds[tokenindex++] = i;
    }
    return tokenIds;
  }

    //try catch vaersion ownerOf. support burned tokenid.
    function tryOwnerOf(uint256 tokenId) external view  virtual returns (address) {
        try this.ownerOf(tokenId) returns (address _address) {
            return(_address);
        } catch {
            return (address(0));//return 0x0 if error.
        }
    }


  /**
    @dev set aa's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__aa(address _owner,uint256 _perc) external virtual onlyOperator {
    _aa = _owner;
    _aaPerc = _perc;
  }

  /**
    @dev set bb's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__bb(address _owner,uint256 _perc) external virtual onlyOperator {
    _bb = _owner;
    _bbPerc = _perc;
  }

  /**
    @dev set cc's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__cc(address _owner,uint256 _perc) external virtual onlyOperator {
    _cc = _owner;
    _ccPerc = _perc;
  }

  /**
    @dev set dd's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__dd(address _owner,uint256 _perc) external virtual onlyOperator {
    _dd = _owner;
    _ddPerc = _perc;
  }

  /**
    @dev set ee's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__ee(address _owner,uint256 _perc) external virtual onlyOperator {
    _ee = _owner;
    _eePerc = _perc;
  }

  /**
    @dev set ff's wallet and fraction.withdraw to this wallet.only operator.
    */
  function setWallet__ff(address _owner,uint256 _perc) external virtual onlyOperator {
    _ff = _owner;
    _ffPerc = _perc;
  }
  /**
    @dev set withdraw's wallet.withdraw to this wallet.only operator.
    */
  function setWallet__ww(address _owner) external virtual onlyOperator {
    _withdrawWallet = _owner;
  }

    //OPENSEA.OPERATORFilterer.START
    /**
     * @notice Set the state of the OpenSea operator filter
     * @param value Flag indicating if the operator filter should be applied to transfers and approvals
     */
    function setOperatorFilteringEnabled(bool value) external onlyOperator {
        operatorFilteringEnabled = value;
    }

    function setApprovalForAll(address operator, bool approved) public override onlyAllowedOperatorApproval(operator) {
        super.setApprovalForAll(operator, approved);
    }

    function approve(address operator, uint256 tokenId) public override onlyAllowedOperatorApproval(operator) {
        super.approve(operator, tokenId);
    }

    function transferFrom(address from, address to, uint256 tokenId) public override onlyAllowedOperator(from) {
        super.transferFrom(from, to, tokenId);
    }

    function safeTransferFrom(address from, address to, uint256 tokenId) public override onlyAllowedOperator(from) {
        super.safeTransferFrom(from, to, tokenId);
    }

    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory data)
        public
        override
        onlyAllowedOperator(from)
    {
        super.safeTransferFrom(from, to, tokenId, data);
    }
    //OPENSEA.OPERATORFilterer.END

    /*///////////////////////////////////////////////////////////////
                    OVERRIDES ERC721RestrictApprove
    //////////////////////////////////////////////////////////////*/
    function addLocalContractAllowList(address transferer)
        external
        override
        onlyOperator
    {
        _addLocalContractAllowList(transferer);
    }

    function removeLocalContractAllowList(address transferer)
        external
        override
        onlyOperator
    {
        _removeLocalContractAllowList(transferer);
    }

    function getLocalContractAllowList()
        external
        override
        view
        returns(address[] memory)
    {
        return _getLocalContractAllowList();
    }

    function setCALLevel(uint256 level) public override onlyOperator {
        CALLevel = level;
    }

    function setCAL(address calAddress) external override onlyOperator {
        _setCAL(calAddress);
    }

    /**
        @dev Operable.Role.ADD
     */
    function grantOperatorRole(address _candidate) external onlyOwner {
        _grantOperatorRole(_candidate);
    }
    /**
        @dev Operable.Role.REMOVE
     */
    function revokeOperatorRole(address _candidate) external onlyOwner {
        _revokeOperatorRole(_candidate);
    }
    
}
//CODE.BY.FRICKLIK