// SPDX-License-Identifier: Unlicense
pragma solidity 0.7.6;
pragma experimental ABIEncoderV2;

import "@openzeppelin/contracts/utils/Counters.sol";
import "../interfaces/IDiamondCut.sol";
import "../libraries/LibDiamond.sol";
import "../libraries/LibGovernance.sol";

contract DiamondCutFacet is IDiamondCut {
    using Counters for Counters.Counter;

    /// @notice Add/replace/remove any number of functions and optionally execute
    ///         a function with delegatecall
    /// @param _diamondCut Contains the facet addresses and function selectors
    /// @param _init The address of the contract or facet to execute _calldata
    /// @param _calldata A function call, including function selector and arguments
    ///                  _calldata is executed with delegatecall on _init
    /// @param _signatures The signatures of between n/2 and n validators for this upgrade
    function diamondCut(
        FacetCut[] calldata _diamondCut,
        address _init,
        bytes calldata _calldata,
        bytes[] calldata _signatures
    ) external override onlyValidSignatures(_signatures.length) {
        bytes32 ethHash = computeDiamondCutMessage(_diamondCut);
        LibGovernance.validateSignatures(ethHash, _signatures);
        LibDiamond.diamondCut(_diamondCut, _init, _calldata);
    }

    ///  @notice Computes the bytes32 ethereum signed message hash of the signature
    function computeDiamondCutMessage(IDiamondCut.FacetCut[] memory _diamondCut) internal view returns (bytes32) {
        LibGovernance.Storage storage gs = LibGovernance.governanceStorage();
        bytes32 hashedData =
            keccak256(
                abi.encode(_diamondCut, gs.administrativeNonce.current())
            );
        return ECDSA.toEthSignedMessageHash(hashedData);
    }

    /// @notice Accepts number of signatures in the range (n/2; n] where n is the number of members
    modifier onlyValidSignatures(uint256 _n) {
        uint256 members = LibGovernance.membersCount();
        require(_n <= members, "Governance: Invalid number of signatures");
        require(_n > members / 2, "Governance: Invalid number of signatures");
        _;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "../math/SafeMath.sol";

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 * Since it is not possible to overflow a 256 bit integer with increments of one, `increment` can skip the {SafeMath}
 * overflow check, thereby saving gas. This does assume however correct usage, in that the underlying `_value` is never
 * directly accessed.
 */
library Counters {
    using SafeMath for uint256;

    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

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

    function increment(Counter storage counter) internal {
        // The {SafeMath} overflow check can be skipped here, see the comment at the top
        counter._value += 1;
    }

    function decrement(Counter storage counter) internal {
        counter._value = counter._value.sub(1);
    }
}

// SPDX-License-Identifier: Unlicense
pragma solidity 0.7.6;
pragma experimental ABIEncoderV2;

interface IDiamondCut {
    enum FacetCutAction {Add, Replace, Remove}
    // Add=0, Replace=1, Remove=2

    struct FacetCut {
        address facetAddress;
        FacetCutAction action;
        bytes4[] functionSelectors;
    }

    /// @notice Add/replace/remove any number of functions and optionally execute
    ///         a function with delegatecall
    /// @param _diamondCut Contains the facet addresses and function selectors
    /// @param _init The address of the contract or facet to execute _calldata
    /// @param _calldata A function call, including function selector and arguments
    ///                  _calldata is executed with delegatecall on _init
    /// @param _signatures The signatures of between n/2 and n validators for this upgrade
    function diamondCut(
        FacetCut[] calldata _diamondCut,
        address _init,
        bytes calldata _calldata,
        bytes[] memory _signatures
    ) external;

    event DiamondCut(FacetCut[] _diamondCut, address _init, bytes _calldata);
}

// SPDX-License-Identifier: Unlicense
pragma solidity 0.7.6;
pragma experimental ABIEncoderV2;

import "../interfaces/IDiamondCut.sol";

library LibDiamond {
    bytes32 constant DIAMOND_STORAGE_POSITION = keccak256("diamond.standard.diamond.storage");

    struct FacetAddressAndPosition {
        address facetAddress;
        uint16 functionSelectorPosition; // position in facetFunctionSelectors.functionSelectors array
    }

    struct FacetFunctionSelectors {
        bytes4[] functionSelectors;
        uint16 facetAddressPosition; // position of facetAddress in facetAddresses array
    }

    struct DiamondStorage {
        // maps function selector to the facet address and
        // the position of the selector in the facetFunctionSelectors.selectors array
        mapping(bytes4 => FacetAddressAndPosition) selectorToFacetAndPosition;
        // maps facet addresses to function selectors
        mapping(address => FacetFunctionSelectors) facetFunctionSelectors;
        // facet addresses
        address[] facetAddresses;
        // Used to query if a contract implements an interface.
        // Used to implement ERC-165.
        mapping(bytes4 => bool) supportedInterfaces;
    }

    function diamondStorage() internal pure returns (DiamondStorage storage ds) {
        bytes32 position = DIAMOND_STORAGE_POSITION;
        assembly {
            ds.slot := position
        }
    }

    event DiamondCut(IDiamondCut.FacetCut[] _diamondCut, address _init, bytes _calldata);

    // Internal function version of diamondCut
    function diamondCut(
        IDiamondCut.FacetCut[] memory _diamondCut,
        address _init,
        bytes memory _calldata
    ) internal {
        for (uint256 facetIndex; facetIndex < _diamondCut.length; facetIndex++) {
            IDiamondCut.FacetCutAction action = _diamondCut[facetIndex].action;
            if (action == IDiamondCut.FacetCutAction.Add) {
                addFunctions(_diamondCut[facetIndex].facetAddress, _diamondCut[facetIndex].functionSelectors);
            } else if (action == IDiamondCut.FacetCutAction.Replace) {
                replaceFunctions(_diamondCut[facetIndex].facetAddress, _diamondCut[facetIndex].functionSelectors);
            } else if (action == IDiamondCut.FacetCutAction.Remove) {
                removeFunctions(_diamondCut[facetIndex].facetAddress, _diamondCut[facetIndex].functionSelectors);
            } else {
                revert("LibDiamondCut: Incorrect FacetCutAction");
            }
        }
        emit DiamondCut(_diamondCut, _init, _calldata);
        initializeDiamondCut(_init, _calldata);
    }

    function addFunctions(address _facetAddress, bytes4[] memory _functionSelectors) internal {
        require(_functionSelectors.length > 0, "LibDiamondCut: No selectors in facet to cut");
        DiamondStorage storage ds = diamondStorage();
        // uint16 selectorCount = uint16(diamondStorage().selectors.length);
        require(_facetAddress != address(0), "LibDiamondCut: Add facet can't be address(0)");
        uint16 selectorPosition = uint16(ds.facetFunctionSelectors[_facetAddress].functionSelectors.length);
        // add new facet address if it does not exist
        if (selectorPosition == 0) {
            enforceHasContractCode(_facetAddress, "LibDiamondCut: New facet has no code");
            ds.facetFunctionSelectors[_facetAddress].facetAddressPosition = uint16(ds.facetAddresses.length);
            ds.facetAddresses.push(_facetAddress);
        }
        for (uint256 selectorIndex; selectorIndex < _functionSelectors.length; selectorIndex++) {
            bytes4 selector = _functionSelectors[selectorIndex];
            address oldFacetAddress = ds.selectorToFacetAndPosition[selector].facetAddress;
            require(oldFacetAddress == address(0), "LibDiamondCut: Can't add function that already exists");
            addFunction(ds, selector, selectorPosition, _facetAddress);
            selectorPosition++;
        }
    }

    function replaceFunctions(address _facetAddress, bytes4[] memory _functionSelectors) internal {
        require(_functionSelectors.length > 0, "LibDiamondCut: No selectors in facet to cut");
        DiamondStorage storage ds = diamondStorage();
        require(_facetAddress != address(0), "LibDiamondCut: Add facet can't be address(0)");
        uint16 selectorPosition = uint16(ds.facetFunctionSelectors[_facetAddress].functionSelectors.length);
        // add new facet address if it does not exist
        if (selectorPosition == 0) {
            enforceHasContractCode(_facetAddress, "LibDiamondCut: New facet has no code");
            ds.facetFunctionSelectors[_facetAddress].facetAddressPosition = uint16(ds.facetAddresses.length);
            ds.facetAddresses.push(_facetAddress);
        }
        for (uint256 selectorIndex; selectorIndex < _functionSelectors.length; selectorIndex++) {
            bytes4 selector = _functionSelectors[selectorIndex];
            address oldFacetAddress = ds.selectorToFacetAndPosition[selector].facetAddress;
            require(oldFacetAddress != _facetAddress, "LibDiamondCut: Can't replace function with same function");
            removeFunction(ds, oldFacetAddress, selector);
            // add function
            addFunction(ds, selector, selectorPosition, _facetAddress);
            selectorPosition++;
        }
    }

    function removeFunctions(address _facetAddress, bytes4[] memory _functionSelectors) internal {
        require(_functionSelectors.length > 0, "LibDiamondCut: No selectors in facet to cut");
        DiamondStorage storage ds = diamondStorage();
        // if function does not exist then do nothing and return
        require(_facetAddress == address(0), "LibDiamondCut: Remove facet address must be address(0)");
        for (uint256 selectorIndex; selectorIndex < _functionSelectors.length; selectorIndex++) {
            bytes4 selector = _functionSelectors[selectorIndex];
            address oldFacetAddress = ds.selectorToFacetAndPosition[selector].facetAddress;
            removeFunction(ds, oldFacetAddress, selector);
        }
    }

    function addFunction(DiamondStorage storage ds, bytes4 _selector, uint16 _selectorPosition, address _facetAddress) internal {
        ds.selectorToFacetAndPosition[_selector].functionSelectorPosition = _selectorPosition;
        ds.facetFunctionSelectors[_facetAddress].functionSelectors.push(_selector);
        ds.selectorToFacetAndPosition[_selector].facetAddress = _facetAddress;
    }

    function removeFunction(DiamondStorage storage ds, address _facetAddress, bytes4 _selector) internal {
        require(_facetAddress != address(0), "LibDiamondCut: Can't remove function that doesn't exist");
        // an immutable function is a function defined directly in a diamond
        require(_facetAddress != address(this), "LibDiamondCut: Can't remove immutable function");
        // replace selector with last selector, then delete last selector
        uint256 selectorPosition = ds.selectorToFacetAndPosition[_selector].functionSelectorPosition;
        uint256 lastSelectorPosition = ds.facetFunctionSelectors[_facetAddress].functionSelectors.length - 1;
        // if not the same then replace _selector with lastSelector
        if (selectorPosition != lastSelectorPosition) {
            bytes4 lastSelector = ds.facetFunctionSelectors[_facetAddress].functionSelectors[lastSelectorPosition];
            ds.facetFunctionSelectors[_facetAddress].functionSelectors[selectorPosition] = lastSelector;
            ds.selectorToFacetAndPosition[lastSelector].functionSelectorPosition = uint16(selectorPosition);
        }
        // delete the last selector
        ds.facetFunctionSelectors[_facetAddress].functionSelectors.pop();
        delete ds.selectorToFacetAndPosition[_selector];

        // if no more selectors for facet address then delete the facet address
        if (lastSelectorPosition == 0) {
            // replace facet address with last facet address and delete last facet address
            uint256 lastFacetAddressPosition = ds.facetAddresses.length - 1;
            uint256 facetAddressPosition = ds.facetFunctionSelectors[_facetAddress].facetAddressPosition;
            if (facetAddressPosition != lastFacetAddressPosition) {
                address lastFacetAddress = ds.facetAddresses[lastFacetAddressPosition];
                ds.facetAddresses[facetAddressPosition] = lastFacetAddress;
                ds.facetFunctionSelectors[lastFacetAddress].facetAddressPosition = uint16(facetAddressPosition);
            }
            ds.facetAddresses.pop();
            delete ds.facetFunctionSelectors[_facetAddress].facetAddressPosition;
        }
    }

    function initializeDiamondCut(address _init, bytes memory _calldata) internal {
        if (_init == address(0)) {
            require(_calldata.length == 0, "LibDiamondCut: _init is address(0) but_calldata is not empty");
        } else {
            require(_calldata.length > 0, "LibDiamondCut: _calldata is empty but _init is not address(0)");
            if (_init != address(this)) {
                enforceHasContractCode(_init, "LibDiamondCut: _init address has no code");
            }
            (bool success, bytes memory error) = _init.delegatecall(_calldata);
            if (!success) {
                if (error.length > 0) {
                    // bubble up the error
                    revert(string(error));
                } else {
                    revert("LibDiamondCut: _init function reverted");
                }
            }
        }
    }

    function enforceHasContractCode(address _contract, string memory _errorMessage) internal view {
        uint256 contractSize;
        assembly {
            contractSize := extcodesize(_contract)
        }
        require(contractSize > 0, _errorMessage);
    }
}

// SPDX-License-Identifier: Unlicense
pragma solidity 0.7.6;
pragma experimental ABIEncoderV2;

import "@openzeppelin/contracts/utils/EnumerableSet.sol";
import "@openzeppelin/contracts/utils/Counters.sol";
import "@openzeppelin/contracts/cryptography/ECDSA.sol";

library LibGovernance {
    using EnumerableSet for EnumerableSet.AddressSet;
    using Counters for Counters.Counter;
    bytes32 constant STORAGE_POSITION = keccak256("governance.storage");

    struct Storage {
        bool initialized;
        // nonce used for making administrative changes
        Counters.Counter administrativeNonce;
        // the set of active validators
        EnumerableSet.AddressSet membersSet;
    }

    function governanceStorage() internal pure returns (Storage storage gs) {
        bytes32 position = STORAGE_POSITION;
        assembly {
            gs.slot := position
        }
    }


    /// @notice Adds/removes a validator from the member set
    function updateMember(address _account, bool _status) internal {
        Storage storage gs = governanceStorage();
        if (_status) {
            require(
                gs.membersSet.add(_account),
                "Governance: Account already added"
            );
        } else if (!_status) {
            require(
                gs.membersSet.length() > 1,
                "Governance: Would become memberless"
            );
            require(
                gs.membersSet.remove(_account),
                "Governance: Account is not a member"
            );
        }
        gs.administrativeNonce.increment();
    }

    /// @notice Computes the bytes32 ethereum signed message hash of the member update message
    function computeMemberUpdateMessage(address _account, bool _status) internal view returns (bytes32) {
        Storage storage gs = governanceStorage();
        bytes32 hashedData =
            keccak256(
                abi.encode(_account, _status, gs.administrativeNonce.current())
            );
        return ECDSA.toEthSignedMessageHash(hashedData);
    }

    /// @notice Returns true/false depending on whether a given address is member or not
    function isMember(address _member) internal view returns (bool) {
        Storage storage gs = governanceStorage();
        return gs.membersSet.contains(_member);
    }

    /// @notice Returns the count of the members
    function membersCount() internal view returns (uint256) {
        Storage storage gs = governanceStorage();
        return gs.membersSet.length();
    }

    /// @notice Returns the address of a member at a given index
    function memberAt(uint256 _index) internal view returns (address) {
        Storage storage gs = governanceStorage();
        return gs.membersSet.at(_index);
    }

    /// @notice Validates the provided signatures aginst the member set
    function validateSignatures(bytes32 _ethHash, bytes[] calldata _signatures) internal view {
        address[] memory signers = new address[](_signatures.length);
        for (uint256 i = 0; i < _signatures.length; i++) {
            address signer = ECDSA.recover(_ethHash, _signatures[i]);
            require(isMember(signer), "Governance: invalid signer");
            for (uint256 j = 0; j < i; j++) {
                require(signer != signers[j], "Governance: duplicate signatures");
            }
            signers[i] = signer;
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) return (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) return 0;
        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");
        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

/**
 * @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.
 */
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;

            // When the value to delete is the last one, the swap operation is unnecessary. However, since this occurs
            // so rarely, we still do the swap anyway to avoid the gas cost of adding an 'if' statement.

            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] = toDeleteIndex + 1; // All indexes are 1-based

            // 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) {
        require(set._values.length > index, "EnumerableSet: index out of bounds");
        return set._values[index];
    }

    // 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);
    }

    // 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))));
    }


    // 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 on 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));
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        // Check the signature length
        if (signature.length != 65) {
            revert("ECDSA: invalid signature length");
        }

        // Divide the signature in r, s and v variables
        bytes32 r;
        bytes32 s;
        uint8 v;

        // ecrecover takes the signature parameters, and the only way to get them
        // currently is to use assembly.
        // solhint-disable-next-line no-inline-assembly
        assembly {
            r := mload(add(signature, 0x20))
            s := mload(add(signature, 0x40))
            v := byte(0, mload(add(signature, 0x60)))
        }

        return recover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover-bytes32-bytes-} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (281): 0 < s < secp256k1n ÷ 2 + 1, and for v in (282): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        require(uint256(s) <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, "ECDSA: invalid signature 's' value");
        require(v == 27 || v == 28, "ECDSA: invalid signature 'v' value");

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        require(signer != address(0), "ECDSA: invalid signature");

        return signer;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * replicates the behavior of the
     * https://github.com/ethereum/wiki/wiki/JSON-RPC#eth_sign[`eth_sign`]
     * JSON-RPC method.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }
}