// File: contracts/governance/GovernanceToken.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/ERC20Votes.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/ERC20Snapshot.sol";
import "@openzeppelin/contracts/access/AccessControl.sol";

contract GovernanceToken is
    ERC20,
    ERC20Permit,
    ERC20Votes,
    ERC20Snapshot,
    AccessControl
{
    bytes32 public constant MINTER_ROLE = keccak256("MINTER_ROLE");
    bytes32 public constant SNAPSHOTER_ROLE = keccak256("SNAPSHOTER_ROLE");

    constructor(
        uint256 initialSupply,
        string memory name,
        string memory symbol
    ) ERC20(name, symbol) ERC20Permit(name) {
        _setupRole(DEFAULT_ADMIN_ROLE, msg.sender);
        _mint(msg.sender, initialSupply);
    }

    function snapshot() external onlyRole(SNAPSHOTER_ROLE) returns (uint256) {
        return _snapshot();
    }

    function mint(address to, uint256 amount) external onlyRole(MINTER_ROLE) {
        _mint(to, amount);
    }

    function burn(address account, uint256 amount) external {
        _burn(account, amount);
    }

    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal override(ERC20, ERC20Snapshot) {
        super._beforeTokenTransfer(from, to, amount);
    }

    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal override(ERC20, ERC20Votes) {
        super._afterTokenTransfer(from, to, amount);
    }

    function _mint(address to, uint256 amount)
        internal
        override(ERC20, ERC20Votes)
    {
        super._mint(to, amount);
    }

    function _burn(address account, uint256 amount)
        internal
        override(ERC20, ERC20Votes)
    {
        super._burn(account, amount);
    }
}

// File: @openzeppelin/contracts/token/ERC20/ERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

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

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, amount);
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, _allowances[owner][spender] + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        address owner = _msgSender();
        uint256 currentAllowance = _allowances[owner][spender];
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `sender` to `recipient`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
        }
        _balances[to] += amount;

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
        }
        _totalSupply -= amount;

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Spend `amount` form the allowance of `owner` toward `spender`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/draft-ERC20Permit.sol)

pragma solidity ^0.8.0;

import "./draft-IERC20Permit.sol";
import "../ERC20.sol";
import "../../../utils/cryptography/draft-EIP712.sol";
import "../../../utils/cryptography/ECDSA.sol";
import "../../../utils/Counters.sol";

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping(address => Counters.Counter) private _nonces;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private immutable _PERMIT_TYPEHASH =
        keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) EIP712(name, "1") {}

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override {
        require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

        bytes32 structHash = keccak256(abi.encode(_PERMIT_TYPEHASH, owner, spender, value, _useNonce(owner), deadline));

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "ERC20Permit: invalid signature");

        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view virtual override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    /**
     * @dev "Consume a nonce": return the current value and increment.
     *
     * _Available since v4.1._
     */
    function _useNonce(address owner) internal virtual returns (uint256 current) {
        Counters.Counter storage nonce = _nonces[owner];
        current = nonce.current();
        nonce.increment();
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/ERC20Votes.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC20/extensions/ERC20Votes.sol)

pragma solidity ^0.8.0;

import "./draft-ERC20Permit.sol";
import "../../../utils/math/Math.sol";
import "../../../governance/utils/IVotes.sol";
import "../../../utils/math/SafeCast.sol";
import "../../../utils/cryptography/ECDSA.sol";

/**
 * @dev Extension of ERC20 to support Compound-like voting and delegation. This version is more generic than Compound's,
 * and supports token supply up to 2^224^ - 1, while COMP is limited to 2^96^ - 1.
 *
 * NOTE: If exact COMP compatibility is required, use the {ERC20VotesComp} variant of this module.
 *
 * This extension keeps a history (checkpoints) of each account's vote power. Vote power can be delegated either
 * by calling the {delegate} function directly, or by providing a signature to be used with {delegateBySig}. Voting
 * power can be queried through the public accessors {getVotes} and {getPastVotes}.
 *
 * By default, token balance does not account for voting power. This makes transfers cheaper. The downside is that it
 * requires users to delegate to themselves in order to activate checkpoints and have their voting power tracked.
 *
 * _Available since v4.2._
 */
abstract contract ERC20Votes is IVotes, ERC20Permit {
    struct Checkpoint {
        uint32 fromBlock;
        uint224 votes;
    }

    bytes32 private constant _DELEGATION_TYPEHASH =
        keccak256("Delegation(address delegatee,uint256 nonce,uint256 expiry)");

    mapping(address => address) private _delegates;
    mapping(address => Checkpoint[]) private _checkpoints;
    Checkpoint[] private _totalSupplyCheckpoints;

    /**
     * @dev Get the `pos`-th checkpoint for `account`.
     */
    function checkpoints(address account, uint32 pos) public view virtual returns (Checkpoint memory) {
        return _checkpoints[account][pos];
    }

    /**
     * @dev Get number of checkpoints for `account`.
     */
    function numCheckpoints(address account) public view virtual returns (uint32) {
        return SafeCast.toUint32(_checkpoints[account].length);
    }

    /**
     * @dev Get the address `account` is currently delegating to.
     */
    function delegates(address account) public view virtual override returns (address) {
        return _delegates[account];
    }

    /**
     * @dev Gets the current votes balance for `account`
     */
    function getVotes(address account) public view virtual override returns (uint256) {
        uint256 pos = _checkpoints[account].length;
        return pos == 0 ? 0 : _checkpoints[account][pos - 1].votes;
    }

    /**
     * @dev Retrieve the number of votes for `account` at the end of `blockNumber`.
     *
     * Requirements:
     *
     * - `blockNumber` must have been already mined
     */
    function getPastVotes(address account, uint256 blockNumber) public view virtual override returns (uint256) {
        require(blockNumber < block.number, "ERC20Votes: block not yet mined");
        return _checkpointsLookup(_checkpoints[account], blockNumber);
    }

    /**
     * @dev Retrieve the `totalSupply` at the end of `blockNumber`. Note, this value is the sum of all balances.
     * It is but NOT the sum of all the delegated votes!
     *
     * Requirements:
     *
     * - `blockNumber` must have been already mined
     */
    function getPastTotalSupply(uint256 blockNumber) public view virtual override returns (uint256) {
        require(blockNumber < block.number, "ERC20Votes: block not yet mined");
        return _checkpointsLookup(_totalSupplyCheckpoints, blockNumber);
    }

    /**
     * @dev Lookup a value in a list of (sorted) checkpoints.
     */
    function _checkpointsLookup(Checkpoint[] storage ckpts, uint256 blockNumber) private view returns (uint256) {
        // We run a binary search to look for the earliest checkpoint taken after `blockNumber`.
        //
        // During the loop, the index of the wanted checkpoint remains in the range [low-1, high).
        // With each iteration, either `low` or `high` is moved towards the middle of the range to maintain the invariant.
        // - If the middle checkpoint is after `blockNumber`, we look in [low, mid)
        // - If the middle checkpoint is before or equal to `blockNumber`, we look in [mid+1, high)
        // Once we reach a single value (when low == high), we've found the right checkpoint at the index high-1, if not
        // out of bounds (in which case we're looking too far in the past and the result is 0).
        // Note that if the latest checkpoint available is exactly for `blockNumber`, we end up with an index that is
        // past the end of the array, so we technically don't find a checkpoint after `blockNumber`, but it works out
        // the same.
        uint256 high = ckpts.length;
        uint256 low = 0;
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (ckpts[mid].fromBlock > blockNumber) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        return high == 0 ? 0 : ckpts[high - 1].votes;
    }

    /**
     * @dev Delegate votes from the sender to `delegatee`.
     */
    function delegate(address delegatee) public virtual override {
        _delegate(_msgSender(), delegatee);
    }

    /**
     * @dev Delegates votes from signer to `delegatee`
     */
    function delegateBySig(
        address delegatee,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override {
        require(block.timestamp <= expiry, "ERC20Votes: signature expired");
        address signer = ECDSA.recover(
            _hashTypedDataV4(keccak256(abi.encode(_DELEGATION_TYPEHASH, delegatee, nonce, expiry))),
            v,
            r,
            s
        );
        require(nonce == _useNonce(signer), "ERC20Votes: invalid nonce");
        _delegate(signer, delegatee);
    }

    /**
     * @dev Maximum token supply. Defaults to `type(uint224).max` (2^224^ - 1).
     */
    function _maxSupply() internal view virtual returns (uint224) {
        return type(uint224).max;
    }

    /**
     * @dev Snapshots the totalSupply after it has been increased.
     */
    function _mint(address account, uint256 amount) internal virtual override {
        super._mint(account, amount);
        require(totalSupply() <= _maxSupply(), "ERC20Votes: total supply risks overflowing votes");

        _writeCheckpoint(_totalSupplyCheckpoints, _add, amount);
    }

    /**
     * @dev Snapshots the totalSupply after it has been decreased.
     */
    function _burn(address account, uint256 amount) internal virtual override {
        super._burn(account, amount);

        _writeCheckpoint(_totalSupplyCheckpoints, _subtract, amount);
    }

    /**
     * @dev Move voting power when tokens are transferred.
     *
     * Emits a {DelegateVotesChanged} event.
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual override {
        super._afterTokenTransfer(from, to, amount);

        _moveVotingPower(delegates(from), delegates(to), amount);
    }

    /**
     * @dev Change delegation for `delegator` to `delegatee`.
     *
     * Emits events {DelegateChanged} and {DelegateVotesChanged}.
     */
    function _delegate(address delegator, address delegatee) internal virtual {
        address currentDelegate = delegates(delegator);
        uint256 delegatorBalance = balanceOf(delegator);
        _delegates[delegator] = delegatee;

        emit DelegateChanged(delegator, currentDelegate, delegatee);

        _moveVotingPower(currentDelegate, delegatee, delegatorBalance);
    }

    function _moveVotingPower(
        address src,
        address dst,
        uint256 amount
    ) private {
        if (src != dst && amount > 0) {
            if (src != address(0)) {
                (uint256 oldWeight, uint256 newWeight) = _writeCheckpoint(_checkpoints[src], _subtract, amount);
                emit DelegateVotesChanged(src, oldWeight, newWeight);
            }

            if (dst != address(0)) {
                (uint256 oldWeight, uint256 newWeight) = _writeCheckpoint(_checkpoints[dst], _add, amount);
                emit DelegateVotesChanged(dst, oldWeight, newWeight);
            }
        }
    }

    function _writeCheckpoint(
        Checkpoint[] storage ckpts,
        function(uint256, uint256) view returns (uint256) op,
        uint256 delta
    ) private returns (uint256 oldWeight, uint256 newWeight) {
        uint256 pos = ckpts.length;
        oldWeight = pos == 0 ? 0 : ckpts[pos - 1].votes;
        newWeight = op(oldWeight, delta);

        if (pos > 0 && ckpts[pos - 1].fromBlock == block.number) {
            ckpts[pos - 1].votes = SafeCast.toUint224(newWeight);
        } else {
            ckpts.push(Checkpoint({fromBlock: SafeCast.toUint32(block.number), votes: SafeCast.toUint224(newWeight)}));
        }
    }

    function _add(uint256 a, uint256 b) private pure returns (uint256) {
        return a + b;
    }

    function _subtract(uint256 a, uint256 b) private pure returns (uint256) {
        return a - b;
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/ERC20Snapshot.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/ERC20Snapshot.sol)

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../../../utils/Arrays.sol";
import "../../../utils/Counters.sol";

/**
 * @dev This contract extends an ERC20 token with a snapshot mechanism. When a snapshot is created, the balances and
 * total supply at the time are recorded for later access.
 *
 * This can be used to safely create mechanisms based on token balances such as trustless dividends or weighted voting.
 * In naive implementations it's possible to perform a "double spend" attack by reusing the same balance from different
 * accounts. By using snapshots to calculate dividends or voting power, those attacks no longer apply. It can also be
 * used to create an efficient ERC20 forking mechanism.
 *
 * Snapshots are created by the internal {_snapshot} function, which will emit the {Snapshot} event and return a
 * snapshot id. To get the total supply at the time of a snapshot, call the function {totalSupplyAt} with the snapshot
 * id. To get the balance of an account at the time of a snapshot, call the {balanceOfAt} function with the snapshot id
 * and the account address.
 *
 * NOTE: Snapshot policy can be customized by overriding the {_getCurrentSnapshotId} method. For example, having it
 * return `block.number` will trigger the creation of snapshot at the begining of each new block. When overridding this
 * function, be careful about the monotonicity of its result. Non-monotonic snapshot ids will break the contract.
 *
 * Implementing snapshots for every block using this method will incur significant gas costs. For a gas-efficient
 * alternative consider {ERC20Votes}.
 *
 * ==== Gas Costs
 *
 * Snapshots are efficient. Snapshot creation is _O(1)_. Retrieval of balances or total supply from a snapshot is _O(log
 * n)_ in the number of snapshots that have been created, although _n_ for a specific account will generally be much
 * smaller since identical balances in subsequent snapshots are stored as a single entry.
 *
 * There is a constant overhead for normal ERC20 transfers due to the additional snapshot bookkeeping. This overhead is
 * only significant for the first transfer that immediately follows a snapshot for a particular account. Subsequent
 * transfers will have normal cost until the next snapshot, and so on.
 */

abstract contract ERC20Snapshot is ERC20 {
    // Inspired by Jordi Baylina's MiniMeToken to record historical balances:
    // https://github.com/Giveth/minimd/blob/ea04d950eea153a04c51fa510b068b9dded390cb/contracts/MiniMeToken.sol

    using Arrays for uint256[];
    using Counters for Counters.Counter;

    // Snapshotted values have arrays of ids and the value corresponding to that id. These could be an array of a
    // Snapshot struct, but that would impede usage of functions that work on an array.
    struct Snapshots {
        uint256[] ids;
        uint256[] values;
    }

    mapping(address => Snapshots) private _accountBalanceSnapshots;
    Snapshots private _totalSupplySnapshots;

    // Snapshot ids increase monotonically, with the first value being 1. An id of 0 is invalid.
    Counters.Counter private _currentSnapshotId;

    /**
     * @dev Emitted by {_snapshot} when a snapshot identified by `id` is created.
     */
    event Snapshot(uint256 id);

    /**
     * @dev Creates a new snapshot and returns its snapshot id.
     *
     * Emits a {Snapshot} event that contains the same id.
     *
     * {_snapshot} is `internal` and you have to decide how to expose it externally. Its usage may be restricted to a
     * set of accounts, for example using {AccessControl}, or it may be open to the public.
     *
     * [WARNING]
     * ====
     * While an open way of calling {_snapshot} is required for certain trust minimization mechanisms such as forking,
     * you must consider that it can potentially be used by attackers in two ways.
     *
     * First, it can be used to increase the cost of retrieval of values from snapshots, although it will grow
     * logarithmically thus rendering this attack ineffective in the long term. Second, it can be used to target
     * specific accounts and increase the cost of ERC20 transfers for them, in the ways specified in the Gas Costs
     * section above.
     *
     * We haven't measured the actual numbers; if this is something you're interested in please reach out to us.
     * ====
     */
    function _snapshot() internal virtual returns (uint256) {
        _currentSnapshotId.increment();

        uint256 currentId = _getCurrentSnapshotId();
        emit Snapshot(currentId);
        return currentId;
    }

    /**
     * @dev Get the current snapshotId
     */
    function _getCurrentSnapshotId() internal view virtual returns (uint256) {
        return _currentSnapshotId.current();
    }

    /**
     * @dev Retrieves the balance of `account` at the time `snapshotId` was created.
     */
    function balanceOfAt(address account, uint256 snapshotId) public view virtual returns (uint256) {
        (bool snapshotted, uint256 value) = _valueAt(snapshotId, _accountBalanceSnapshots[account]);

        return snapshotted ? value : balanceOf(account);
    }

    /**
     * @dev Retrieves the total supply at the time `snapshotId` was created.
     */
    function totalSupplyAt(uint256 snapshotId) public view virtual returns (uint256) {
        (bool snapshotted, uint256 value) = _valueAt(snapshotId, _totalSupplySnapshots);

        return snapshotted ? value : totalSupply();
    }

    // Update balance and/or total supply snapshots before the values are modified. This is implemented
    // in the _beforeTokenTransfer hook, which is executed for _mint, _burn, and _transfer operations.
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual override {
        super._beforeTokenTransfer(from, to, amount);

        if (from == address(0)) {
            // mint
            _updateAccountSnapshot(to);
            _updateTotalSupplySnapshot();
        } else if (to == address(0)) {
            // burn
            _updateAccountSnapshot(from);
            _updateTotalSupplySnapshot();
        } else {
            // transfer
            _updateAccountSnapshot(from);
            _updateAccountSnapshot(to);
        }
    }

    function _valueAt(uint256 snapshotId, Snapshots storage snapshots) private view returns (bool, uint256) {
        require(snapshotId > 0, "ERC20Snapshot: id is 0");
        require(snapshotId <= _getCurrentSnapshotId(), "ERC20Snapshot: nonexistent id");

        // When a valid snapshot is queried, there are three possibilities:
        //  a) The queried value was not modified after the snapshot was taken. Therefore, a snapshot entry was never
        //  created for this id, and all stored snapshot ids are smaller than the requested one. The value that corresponds
        //  to this id is the current one.
        //  b) The queried value was modified after the snapshot was taken. Therefore, there will be an entry with the
        //  requested id, and its value is the one to return.
        //  c) More snapshots were created after the requested one, and the queried value was later modified. There will be
        //  no entry for the requested id: the value that corresponds to it is that of the smallest snapshot id that is
        //  larger than the requested one.
        //
        // In summary, we need to find an element in an array, returning the index of the smallest value that is larger if
        // it is not found, unless said value doesn't exist (e.g. when all values are smaller). Arrays.findUpperBound does
        // exactly this.

        uint256 index = snapshots.ids.findUpperBound(snapshotId);

        if (index == snapshots.ids.length) {
            return (false, 0);
        } else {
            return (true, snapshots.values[index]);
        }
    }

    function _updateAccountSnapshot(address account) private {
        _updateSnapshot(_accountBalanceSnapshots[account], balanceOf(account));
    }

    function _updateTotalSupplySnapshot() private {
        _updateSnapshot(_totalSupplySnapshots, totalSupply());
    }

    function _updateSnapshot(Snapshots storage snapshots, uint256 currentValue) private {
        uint256 currentId = _getCurrentSnapshotId();
        if (_lastSnapshotId(snapshots.ids) < currentId) {
            snapshots.ids.push(currentId);
            snapshots.values.push(currentValue);
        }
    }

    function _lastSnapshotId(uint256[] storage ids) private view returns (uint256) {
        if (ids.length == 0) {
            return 0;
        } else {
            return ids[ids.length - 1];
        }
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role, _msgSender());
        _;
    }

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

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);

    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);
}

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

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

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/draft-IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// File: @openzeppelin/contracts/utils/cryptography/draft-EIP712.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/cryptography/draft-EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSA.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;
    address private immutable _CACHED_THIS;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;

    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256(
            "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
        );
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = block.chainid;
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _CACHED_THIS = address(this);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _CACHED_THIS && block.chainid == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @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 {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        } else if (error == RecoverError.InvalidSignatureV) {
            revert("ECDSA: invalid signature 'v' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. 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.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        // Check the signature length
        // - case 65: r,s,v signature (standard)
        // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098) _Available since v4.1._
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else if (signature.length == 64) {
            bytes32 r;
            bytes32 vs;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            assembly {
                r := mload(add(signature, 0x20))
                vs := mload(add(signature, 0x40))
            }
            return tryRecover(hash, r, vs);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @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) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // 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 (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): 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.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }
        if (v != 27 && v != 28) {
            return (address(0), RecoverError.InvalidSignatureV);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * 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));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Counters.sol)

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. 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;`
 */
library Counters {
    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 {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Strings.sol)

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @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] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @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 / b + (a % b == 0 ? 0 : 1);
    }
}

// File: @openzeppelin/contracts/governance/utils/IVotes.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (governance/utils/IVotes.sol)
pragma solidity ^0.8.0;

/**
 * @dev Common interface for {ERC20Votes}, {ERC721Votes}, and other {Votes}-enabled contracts.
 *
 * _Available since v4.5._
 */
interface IVotes {
    /**
     * @dev Emitted when an account changes their delegate.
     */
    event DelegateChanged(address indexed delegator, address indexed fromDelegate, address indexed toDelegate);

    /**
     * @dev Emitted when a token transfer or delegate change results in changes to a delegate's number of votes.
     */
    event DelegateVotesChanged(address indexed delegate, uint256 previousBalance, uint256 newBalance);

    /**
     * @dev Returns the current amount of votes that `account` has.
     */
    function getVotes(address account) external view returns (uint256);

    /**
     * @dev Returns the amount of votes that `account` had at the end of a past block (`blockNumber`).
     */
    function getPastVotes(address account, uint256 blockNumber) external view returns (uint256);

    /**
     * @dev Returns the total supply of votes available at the end of a past block (`blockNumber`).
     *
     * NOTE: This value is the sum of all available votes, which is not necessarily the sum of all delegated votes.
     * Votes that have not been delegated are still part of total supply, even though they would not participate in a
     * vote.
     */
    function getPastTotalSupply(uint256 blockNumber) external view returns (uint256);

    /**
     * @dev Returns the delegate that `account` has chosen.
     */
    function delegates(address account) external view returns (address);

    /**
     * @dev Delegates votes from the sender to `delegatee`.
     */
    function delegate(address delegatee) external;

    /**
     * @dev Delegates votes from signer to `delegatee`.
     */
    function delegateBySig(
        address delegatee,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/math/SafeCast.sol)

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such 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.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= type(int128).min && value <= type(int128).max, "SafeCast: value doesn't fit in 128 bits");
        return int128(value);
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= type(int64).min && value <= type(int64).max, "SafeCast: value doesn't fit in 64 bits");
        return int64(value);
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= type(int32).min && value <= type(int32).max, "SafeCast: value doesn't fit in 32 bits");
        return int32(value);
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= type(int16).min && value <= type(int16).max, "SafeCast: value doesn't fit in 16 bits");
        return int16(value);
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= type(int8).min && value <= type(int8).max, "SafeCast: value doesn't fit in 8 bits");
        return int8(value);
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Arrays.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

/**
 * @dev Collection of functions related to array types.
 */
library Arrays {
    /**
     * @dev Searches a sorted `array` and returns the first index that contains
     * a value greater or equal to `element`. If no such index exists (i.e. all
     * values in the array are strictly less than `element`), the array length is
     * returned. Time complexity O(log n).
     *
     * `array` is expected to be sorted in ascending order, and to contain no
     * repeated elements.
     */
    function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        if (array.length == 0) {
            return 0;
        }

        uint256 low = 0;
        uint256 high = array.length;

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds down (it does integer division with truncation).
            if (array[mid] > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && array[low - 1] == element) {
            return low - 1;
        } else {
            return low;
        }
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @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/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT
// 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);
}