// File: lib/openzeppelin-contracts/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

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

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

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

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

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

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

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

// File: lib/openzeppelin-contracts/contracts/token/ERC20/ERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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.openzeppelin.com/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, allowance(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 = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `from` to `to`.
     *
     * 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;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _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;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _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;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _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 Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * 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: lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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);

    /**
     * @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);
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/extensions/draft-ERC20Permit.sol)

pragma solidity ^0.8.0;

import "./draft-IERC20Permit.sol";
import "../ERC20.sol";
import "../../../utils/cryptography/ECDSA.sol";
import "../../../utils/cryptography/EIP712.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 constant _PERMIT_TYPEHASH =
        keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    /**
     * @dev In previous versions `_PERMIT_TYPEHASH` was declared as `immutable`.
     * However, to ensure consistency with the upgradeable transpiler, we will continue
     * to reserve a slot.
     * @custom:oz-renamed-from _PERMIT_TYPEHASH
     */
    // solhint-disable-next-line var-name-mixedcase
    bytes32 private _PERMIT_TYPEHASH_DEPRECATED_SLOT;

    /**
     * @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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/draft-IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: lib/openzeppelin-contracts/contracts/token/ERC721/IERC721.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

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

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

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

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

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

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

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

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

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

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

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

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

// File: lib/openzeppelin-contracts/contracts/token/ERC721/extensions/IERC721Enumerable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/extensions/IERC721Enumerable.sol)

pragma solidity ^0.8.0;

import "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Enumerable is IERC721 {
    /**
     * @dev Returns the total amount of tokens stored by the contract.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns a token ID owned by `owner` at a given `index` of its token list.
     * Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index) external view returns (uint256);

    /**
     * @dev Returns a token ID at a given `index` of all the tokens stored by the contract.
     * Use along with {totalSupply} to enumerate all tokens.
     */
    function tokenByIndex(uint256 index) external view returns (uint256);
}

// File: lib/openzeppelin-contracts/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

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

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

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

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

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

// File: lib/openzeppelin-contracts/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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 // Deprecated in v4.8
    }

    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");
        }
    }

    /**
     * @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) {
        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.
            /// @solidity memory-safe-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 {
            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 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: lib/openzeppelin-contracts/contracts/utils/cryptography/EIP712.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/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: lib/openzeppelin-contracts/contracts/utils/cryptography/MerkleProof.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/MerkleProof.sol)

pragma solidity ^0.8.0;

/**
 * @dev These functions deal with verification of Merkle Tree proofs.
 *
 * The tree and the proofs can be generated using our
 * https://github.com/OpenZeppelin/merkle-tree[JavaScript library].
 * You will find a quickstart guide in the readme.
 *
 * WARNING: You should avoid using leaf values that are 64 bytes long prior to
 * hashing, or use a hash function other than keccak256 for hashing leaves.
 * This is because the concatenation of a sorted pair of internal nodes in
 * the merkle tree could be reinterpreted as a leaf value.
 * OpenZeppelin's JavaScript library generates merkle trees that are safe
 * against this attack out of the box.
 */
library MerkleProof {
    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     */
    function verify(
        bytes32[] memory proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProof(proof, leaf) == root;
    }

    /**
     * @dev Calldata version of {verify}
     *
     * _Available since v4.7._
     */
    function verifyCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProofCalldata(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leafs & pre-images are assumed to be sorted.
     *
     * _Available since v4.4._
     */
    function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Calldata version of {processProof}
     *
     * _Available since v4.7._
     */
    function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProof(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Calldata version of {multiProofVerify}
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * CAUTION: Not all merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * _Available since v4.7._
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Calldata version of {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {
        return a < b ? _efficientHash(a, b) : _efficientHash(b, a);
    }

    function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}

// File: lib/openzeppelin-contracts/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);
}

// File: lib/openzeppelin-contracts/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: lib/v3-core/contracts/interfaces/IUniswapV3Pool.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import {IUniswapV3PoolImmutables} from './pool/IUniswapV3PoolImmutables.sol';
import {IUniswapV3PoolState} from './pool/IUniswapV3PoolState.sol';
import {IUniswapV3PoolDerivedState} from './pool/IUniswapV3PoolDerivedState.sol';
import {IUniswapV3PoolActions} from './pool/IUniswapV3PoolActions.sol';
import {IUniswapV3PoolOwnerActions} from './pool/IUniswapV3PoolOwnerActions.sol';
import {IUniswapV3PoolErrors} from './pool/IUniswapV3PoolErrors.sol';
import {IUniswapV3PoolEvents} from './pool/IUniswapV3PoolEvents.sol';

/// @title The interface for a Uniswap V3 Pool
/// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform
/// to the ERC20 specification
/// @dev The pool interface is broken up into many smaller pieces
interface IUniswapV3Pool is
    IUniswapV3PoolImmutables,
    IUniswapV3PoolState,
    IUniswapV3PoolDerivedState,
    IUniswapV3PoolActions,
    IUniswapV3PoolOwnerActions,
    IUniswapV3PoolErrors,
    IUniswapV3PoolEvents
{

}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface IUniswapV3PoolActions {
    /// @notice Sets the initial price for the pool
    /// @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value
    /// @param sqrtPriceX96 the initial sqrt price of the pool as a Q64.96
    function initialize(uint160 sqrtPriceX96) external;

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @dev The caller of this method receives a callback in the form of IUniswapV3MintCallback#uniswapV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
    /// on tickLower, tickUpper, the amount of liquidity, and the current price.
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    /// @param data Any data that should be passed through to the callback
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Collects tokens owed to a position
    /// @dev Does not recompute fees earned, which must be done either via mint or burn of any amount of liquidity.
    /// Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
    /// amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
    /// actual tokens owed, e.g. type(uint128).max. Tokens owed may be from accumulated swap fees or burned liquidity.
    /// @param recipient The address which should receive the fees collected
    /// @param tickLower The lower tick of the position for which to collect fees
    /// @param tickUpper The upper tick of the position for which to collect fees
    /// @param amount0Requested How much token0 should be withdrawn from the fees owed
    /// @param amount1Requested How much token1 should be withdrawn from the fees owed
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);

    /// @notice Burn liquidity from the sender and account tokens owed for the liquidity to the position
    /// @dev Can be used to trigger a recalculation of fees owed to a position by calling with an amount of 0
    /// @dev Fees must be collected separately via a call to #collect
    /// @param tickLower The lower tick of the position for which to burn liquidity
    /// @param tickUpper The upper tick of the position for which to burn liquidity
    /// @param amount How much liquidity to burn
    /// @return amount0 The amount of token0 sent to the recipient
    /// @return amount1 The amount of token1 sent to the recipient
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// @dev The caller of this method receives a callback in the form of IUniswapV3SwapCallback#uniswapV3SwapCallback
    /// @param recipient The address to receive the output of the swap
    /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0
    /// @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
    /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
    /// value after the swap. If one for zero, the price cannot be greater than this value after the swap
    /// @param data Any data to be passed through to the callback
    /// @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
    /// @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Receive token0 and/or token1 and pay it back, plus a fee, in the callback
    /// @dev The caller of this method receives a callback in the form of IUniswapV3FlashCallback#uniswapV3FlashCallback
    /// @dev Can be used to donate underlying tokens pro-rata to currently in-range liquidity providers by calling
    /// with 0 amount{0,1} and sending the donation amount(s) from the callback
    /// @param recipient The address which will receive the token0 and token1 amounts
    /// @param amount0 The amount of token0 to send
    /// @param amount1 The amount of token1 to send
    /// @param data Any data to be passed through to the callback
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external;

    /// @notice Increase the maximum number of price and liquidity observations that this pool will store
    /// @dev This method is no-op if the pool already has an observationCardinalityNext greater than or equal to
    /// the input observationCardinalityNext.
    /// @param observationCardinalityNext The desired minimum number of observations for the pool to store
    function increaseObservationCardinalityNext(uint16 observationCardinalityNext) external;
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolDerivedState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that is not stored
/// @notice Contains view functions to provide information about the pool that is computed rather than stored on the
/// blockchain. The functions here may have variable gas costs.
interface IUniswapV3PoolDerivedState {
    /// @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
    /// @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
    /// the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
    /// you must call it with secondsAgos = [3600, 0].
    /// @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
    /// log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
    /// @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
    /// @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
    /// @return secondsPerLiquidityCumulativeX128s Cumulative seconds per liquidity-in-range value as of each `secondsAgos` from the current block
    /// timestamp
    function observe(uint32[] calldata secondsAgos)
        external
        view
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);

    /// @notice Returns a snapshot of the tick cumulative, seconds per liquidity and seconds inside a tick range
    /// @dev Snapshots must only be compared to other snapshots, taken over a period for which a position existed.
    /// I.e., snapshots cannot be compared if a position is not held for the entire period between when the first
    /// snapshot is taken and the second snapshot is taken.
    /// @param tickLower The lower tick of the range
    /// @param tickUpper The upper tick of the range
    /// @return tickCumulativeInside The snapshot of the tick accumulator for the range
    /// @return secondsPerLiquidityInsideX128 The snapshot of seconds per liquidity for the range
    /// @return secondsInside The snapshot of seconds per liquidity for the range
    function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)
        external
        view
        returns (
            int56 tickCumulativeInside,
            uint160 secondsPerLiquidityInsideX128,
            uint32 secondsInside
        );
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolErrors.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Errors emitted by a pool
/// @notice Contains all events emitted by the pool
interface IUniswapV3PoolErrors {
    error LOK();
    error TLU();
    error TLM();
    error TUM();
    error AI();
    error M0();
    error M1();
    error AS();
    error IIA();
    error L();
    error F0();
    error F1();
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolEvents.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Events emitted by a pool
/// @notice Contains all events emitted by the pool
interface IUniswapV3PoolEvents {
    /// @notice Emitted exactly once by a pool when #initialize is first called on the pool
    /// @dev Mint/Burn/Swap cannot be emitted by the pool before Initialize
    /// @param sqrtPriceX96 The initial sqrt price of the pool, as a Q64.96
    /// @param tick The initial tick of the pool, i.e. log base 1.0001 of the starting price of the pool
    event Initialize(uint160 sqrtPriceX96, int24 tick);

    /// @notice Emitted when liquidity is minted for a given position
    /// @param sender The address that minted the liquidity
    /// @param owner The owner of the position and recipient of any minted liquidity
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity minted to the position range
    /// @param amount0 How much token0 was required for the minted liquidity
    /// @param amount1 How much token1 was required for the minted liquidity
    event Mint(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted when fees are collected by the owner of a position
    /// @dev Collect events may be emitted with zero amount0 and amount1 when the caller chooses not to collect fees
    /// @param owner The owner of the position for which fees are collected
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount0 The amount of token0 fees collected
    /// @param amount1 The amount of token1 fees collected
    event Collect(
        address indexed owner,
        address recipient,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount0,
        uint128 amount1
    );

    /// @notice Emitted when a position's liquidity is removed
    /// @dev Does not withdraw any fees earned by the liquidity position, which must be withdrawn via #collect
    /// @param owner The owner of the position for which liquidity is removed
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity to remove
    /// @param amount0 The amount of token0 withdrawn
    /// @param amount1 The amount of token1 withdrawn
    event Burn(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted by the pool for any swaps between token0 and token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the output of the swap
    /// @param amount0 The delta of the token0 balance of the pool
    /// @param amount1 The delta of the token1 balance of the pool
    /// @param sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96
    /// @param liquidity The liquidity of the pool after the swap
    /// @param tick The log base 1.0001 of price of the pool after the swap
    event Swap(
        address indexed sender,
        address indexed recipient,
        int256 amount0,
        int256 amount1,
        uint160 sqrtPriceX96,
        uint128 liquidity,
        int24 tick
    );

    /// @notice Emitted by the pool for any flashes of token0/token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the tokens from flash
    /// @param amount0 The amount of token0 that was flashed
    /// @param amount1 The amount of token1 that was flashed
    /// @param paid0 The amount of token0 paid for the flash, which can exceed the amount0 plus the fee
    /// @param paid1 The amount of token1 paid for the flash, which can exceed the amount1 plus the fee
    event Flash(
        address indexed sender,
        address indexed recipient,
        uint256 amount0,
        uint256 amount1,
        uint256 paid0,
        uint256 paid1
    );

    /// @notice Emitted by the pool for increases to the number of observations that can be stored
    /// @dev observationCardinalityNext is not the observation cardinality until an observation is written at the index
    /// just before a mint/swap/burn.
    /// @param observationCardinalityNextOld The previous value of the next observation cardinality
    /// @param observationCardinalityNextNew The updated value of the next observation cardinality
    event IncreaseObservationCardinalityNext(
        uint16 observationCardinalityNextOld,
        uint16 observationCardinalityNextNew
    );

    /// @notice Emitted when the protocol fee is changed by the pool
    /// @param feeProtocol0Old The previous value of the token0 protocol fee
    /// @param feeProtocol1Old The previous value of the token1 protocol fee
    /// @param feeProtocol0New The updated value of the token0 protocol fee
    /// @param feeProtocol1New The updated value of the token1 protocol fee
    event SetFeeProtocol(uint8 feeProtocol0Old, uint8 feeProtocol1Old, uint8 feeProtocol0New, uint8 feeProtocol1New);

    /// @notice Emitted when the collected protocol fees are withdrawn by the factory owner
    /// @param sender The address that collects the protocol fees
    /// @param recipient The address that receives the collected protocol fees
    /// @param amount0 The amount of token0 protocol fees that is withdrawn
    /// @param amount0 The amount of token1 protocol fees that is withdrawn
    event CollectProtocol(address indexed sender, address indexed recipient, uint128 amount0, uint128 amount1);
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolImmutables.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that never changes
/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values
interface IUniswapV3PoolImmutables {
    /// @notice The contract that deployed the pool, which must adhere to the IUniswapV3Factory interface
    /// @return The contract address
    function factory() external view returns (address);

    /// @notice The first of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token0() external view returns (address);

    /// @notice The second of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token1() external view returns (address);

    /// @notice The pool's fee in hundredths of a bip, i.e. 1e-6
    /// @return The fee
    function fee() external view returns (uint24);

    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);

    /// @notice The maximum amount of position liquidity that can use any tick in the range
    /// @dev This parameter is enforced per tick to prevent liquidity from overflowing a uint128 at any point, and
    /// also prevents out-of-range liquidity from being used to prevent adding in-range liquidity to a pool
    /// @return The max amount of liquidity per tick
    function maxLiquidityPerTick() external view returns (uint128);
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolOwnerActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissioned pool actions
/// @notice Contains pool methods that may only be called by the factory owner
interface IUniswapV3PoolOwnerActions {
    /// @notice Set the denominator of the protocol's % share of the fees
    /// @param feeProtocol0 new protocol fee for token0 of the pool
    /// @param feeProtocol1 new protocol fee for token1 of the pool
    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external;

    /// @notice Collect the protocol fee accrued to the pool
    /// @param recipient The address to which collected protocol fees should be sent
    /// @param amount0Requested The maximum amount of token0 to send, can be 0 to collect fees in only token1
    /// @param amount1Requested The maximum amount of token1 to send, can be 0 to collect fees in only token0
    /// @return amount0 The protocol fee collected in token0
    /// @return amount1 The protocol fee collected in token1
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);
}

// File: lib/v3-core/contracts/interfaces/pool/IUniswapV3PoolState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that can change
/// @notice These methods compose the pool's state, and can change with any frequency including multiple times
/// per transaction
interface IUniswapV3PoolState {
    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas
    /// when accessed externally.
    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value
    /// @return tick The current tick of the pool, i.e. according to the last tick transition that was run.
    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick
    /// boundary.
    /// @return observationIndex The index of the last oracle observation that was written,
    /// @return observationCardinality The current maximum number of observations stored in the pool,
    /// @return observationCardinalityNext The next maximum number of observations, to be updated when the observation.
    /// @return feeProtocol The protocol fee for both tokens of the pool.
    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0
    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0()
        external
        view
        returns (
            uint160 sqrtPriceX96,
            int24 tick,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext,
            uint8 feeProtocol,
            bool unlocked
        );

    /// @notice The fee growth as a Q128.128 fees of token0 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal0X128() external view returns (uint256);

    /// @notice The fee growth as a Q128.128 fees of token1 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal1X128() external view returns (uint256);

    /// @notice The amounts of token0 and token1 that are owed to the protocol
    /// @dev Protocol fees will never exceed uint128 max in either token
    function protocolFees() external view returns (uint128 token0, uint128 token1);

    /// @notice The currently in range liquidity available to the pool
    /// @dev This value has no relationship to the total liquidity across all ticks
    /// @return The liquidity at the current price of the pool
    function liquidity() external view returns (uint128);

    /// @notice Look up information about a specific tick in the pool
    /// @param tick The tick to look up
    /// @return liquidityGross the total amount of position liquidity that uses the pool either as tick lower or
    /// tick upper
    /// @return liquidityNet how much liquidity changes when the pool price crosses the tick,
    /// @return feeGrowthOutside0X128 the fee growth on the other side of the tick from the current tick in token0,
    /// @return feeGrowthOutside1X128 the fee growth on the other side of the tick from the current tick in token1,
    /// @return tickCumulativeOutside the cumulative tick value on the other side of the tick from the current tick
    /// @return secondsPerLiquidityOutsideX128 the seconds spent per liquidity on the other side of the tick from the current tick,
    /// @return secondsOutside the seconds spent on the other side of the tick from the current tick,
    /// @return initialized Set to true if the tick is initialized, i.e. liquidityGross is greater than 0, otherwise equal to false.
    /// Outside values can only be used if the tick is initialized, i.e. if liquidityGross is greater than 0.
    /// In addition, these values are only relative and must be used only in comparison to previous snapshots for
    /// a specific position.
    function ticks(int24 tick)
        external
        view
        returns (
            uint128 liquidityGross,
            int128 liquidityNet,
            uint256 feeGrowthOutside0X128,
            uint256 feeGrowthOutside1X128,
            int56 tickCumulativeOutside,
            uint160 secondsPerLiquidityOutsideX128,
            uint32 secondsOutside,
            bool initialized
        );

    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information
    function tickBitmap(int16 wordPosition) external view returns (uint256);

    /// @notice Returns the information about a position by the position's key
    /// @param key The position's key is a hash of a preimage composed by the owner, tickLower and tickUpper
    /// @return liquidity The amount of liquidity in the position,
    /// @return feeGrowthInside0LastX128 fee growth of token0 inside the tick range as of the last mint/burn/poke,
    /// @return feeGrowthInside1LastX128 fee growth of token1 inside the tick range as of the last mint/burn/poke,
    /// @return tokensOwed0 the computed amount of token0 owed to the position as of the last mint/burn/poke,
    /// @return tokensOwed1 the computed amount of token1 owed to the position as of the last mint/burn/poke
    function positions(bytes32 key)
        external
        view
        returns (
            uint128 liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        );

    /// @notice Returns data about a specific observation index
    /// @param index The element of the observations array to fetch
    /// @dev You most likely want to use #observe() instead of this method to get an observation as of some amount of time
    /// ago, rather than at a specific index in the array.
    /// @return blockTimestamp The timestamp of the observation,
    /// @return tickCumulative the tick multiplied by seconds elapsed for the life of the pool as of the observation timestamp,
    /// @return secondsPerLiquidityCumulativeX128 the seconds per in range liquidity for the life of the pool as of the observation timestamp,
    /// @return initialized whether the observation has been initialized and the values are safe to use
    function observations(uint256 index)
        external
        view
        returns (
            uint32 blockTimestamp,
            int56 tickCumulative,
            uint160 secondsPerLiquidityCumulativeX128,
            bool initialized
        );
}

// File: lib/v3-core/contracts/libraries/FullMath.sol



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

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = a * b
            // Compute the product mod 2**256 and mod 2**256 - 1
            // then use the Chinese Remainder Theorem to reconstruct
            // the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2**256 + prod0
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(a, b, not(0))
                prod0 := mul(a, b)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division
            if (prod1 == 0) {
                require(denominator > 0);
                assembly {
                    result := div(prod0, denominator)
                }
                return result;
            }

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

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

            // Make division exact by subtracting the remainder from [prod1 prod0]
            // Compute remainder using mulmod
            uint256 remainder;
            assembly {
                remainder := mulmod(a, b, denominator)
            }
            // Subtract 256 bit number from 512 bit number
            assembly {
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator
            // Compute largest power of two divisor of denominator.
            // Always >= 1.
            uint256 twos = (0 - denominator) & denominator;
            // Divide denominator by power of two
            assembly {
                denominator := div(denominator, twos)
            }

            // Divide [prod1 prod0] by the factors of two
            assembly {
                prod0 := div(prod0, twos)
            }
            // Shift in bits from prod1 into prod0. For this we need
            // to flip `twos` such that it is 2**256 / twos.
            // If twos is zero, then it becomes one
            assembly {
                twos := add(div(sub(0, twos), twos), 1)
            }
            prod0 |= prod1 * twos;

            // Invert denominator mod 2**256
            // Now that denominator is an odd number, it has an inverse
            // modulo 2**256 such that denominator * inv = 1 mod 2**256.
            // Compute the inverse by starting with a seed that is correct
            // correct for four bits. That is, denominator * inv = 1 mod 2**4
            uint256 inv = (3 * denominator) ^ 2;
            // Now use Newton-Raphson iteration to improve the precision.
            // Thanks to Hensel's lifting lemma, this also works in modular
            // arithmetic, doubling the correct bits in each step.
            inv *= 2 - denominator * inv; // inverse mod 2**8
            inv *= 2 - denominator * inv; // inverse mod 2**16
            inv *= 2 - denominator * inv; // inverse mod 2**32
            inv *= 2 - denominator * inv; // inverse mod 2**64
            inv *= 2 - denominator * inv; // inverse mod 2**128
            inv *= 2 - denominator * inv; // inverse mod 2**256

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

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            result = mulDiv(a, b, denominator);
            if (mulmod(a, b, denominator) > 0) {
                require(result < type(uint256).max);
                result++;
            }
        }
    }
}

// File: lib/v3-core/contracts/libraries/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
library TickMath {
    error T();
    error R();

    /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
    int24 internal constant MIN_TICK = -887272;
    /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
    int24 internal constant MAX_TICK = -MIN_TICK;

    /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
    uint160 internal constant MIN_SQRT_RATIO = 4295128739;
    /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
    uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
        unchecked {
            uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
            if (absTick > uint256(int256(MAX_TICK))) revert T();

            uint256 ratio = absTick & 0x1 != 0
                ? 0xfffcb933bd6fad37aa2d162d1a594001
                : 0x100000000000000000000000000000000;
            if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
            if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
            if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
            if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
            if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
            if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
            if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
            if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
            if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
            if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
            if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
            if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
            if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
            if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
            if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
            if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
            if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
            if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
            if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;

            if (tick > 0) ratio = type(uint256).max / ratio;

            // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
            // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
            // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
            sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
        }
    }

    /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
    /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
    /// ever return.
    /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96
    /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
    function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
        unchecked {
            // second inequality must be < because the price can never reach the price at the max tick
            if (!(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO)) revert R();
            uint256 ratio = uint256(sqrtPriceX96) << 32;

            uint256 r = ratio;
            uint256 msb = 0;

            assembly {
                let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(5, gt(r, 0xFFFFFFFF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(4, gt(r, 0xFFFF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(3, gt(r, 0xFF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(2, gt(r, 0xF))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := shl(1, gt(r, 0x3))
                msb := or(msb, f)
                r := shr(f, r)
            }
            assembly {
                let f := gt(r, 0x1)
                msb := or(msb, f)
            }

            if (msb >= 128) r = ratio >> (msb - 127);
            else r = ratio << (127 - msb);

            int256 log_2 = (int256(msb) - 128) << 64;

            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(63, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(62, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(61, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(60, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(59, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(58, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(57, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(56, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(55, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(54, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(53, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(52, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(51, f))
                r := shr(f, r)
            }
            assembly {
                r := shr(127, mul(r, r))
                let f := shr(128, r)
                log_2 := or(log_2, shl(50, f))
            }

            int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

            int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
            int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);

            tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
        }
    }
}

// File: lib/v3-periphery/contracts/libraries/OracleLibrary.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.9.0;

import '@uniswap/v3-core/contracts/libraries/FullMath.sol';
import '@uniswap/v3-core/contracts/libraries/TickMath.sol';
import '@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol';

/// @title Oracle library
/// @notice Provides functions to integrate with V3 pool oracle
library OracleLibrary {
    /// @notice Calculates time-weighted means of tick and liquidity for a given Uniswap V3 pool
    /// @param pool Address of the pool that we want to observe
    /// @param secondsAgo Number of seconds in the past from which to calculate the time-weighted means
    /// @return arithmeticMeanTick The arithmetic mean tick from (block.timestamp - secondsAgo) to block.timestamp
    /// @return harmonicMeanLiquidity The harmonic mean liquidity from (block.timestamp - secondsAgo) to block.timestamp
    function consult(address pool, uint32 secondsAgo)
        internal
        view
        returns (int24 arithmeticMeanTick, uint128 harmonicMeanLiquidity)
    {
        require(secondsAgo != 0, 'BP');

        uint32[] memory secondsAgos = new uint32[](2);
        secondsAgos[0] = secondsAgo;
        secondsAgos[1] = 0;

        (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s) = IUniswapV3Pool(pool)
            .observe(secondsAgos);

        int56 tickCumulativesDelta = tickCumulatives[1] - tickCumulatives[0];
        uint160 secondsPerLiquidityCumulativesDelta = secondsPerLiquidityCumulativeX128s[1] -
            secondsPerLiquidityCumulativeX128s[0];

        arithmeticMeanTick = int24(tickCumulativesDelta / int56(uint56(secondsAgo)));
        // Always round to negative infinity
        if (tickCumulativesDelta < 0 && (tickCumulativesDelta % int56(uint56(secondsAgo)) != 0)) arithmeticMeanTick--;

        // We are multiplying here instead of shifting to ensure that harmonicMeanLiquidity doesn't overflow uint128
        uint192 secondsAgoX160 = uint192(secondsAgo) * type(uint160).max;
        harmonicMeanLiquidity = uint128(secondsAgoX160 / (uint192(secondsPerLiquidityCumulativesDelta) << 32));
    }

    /// @notice Given a tick and a token amount, calculates the amount of token received in exchange
    /// @param tick Tick value used to calculate the quote
    /// @param baseAmount Amount of token to be converted
    /// @param baseToken Address of an ERC20 token contract used as the baseAmount denomination
    /// @param quoteToken Address of an ERC20 token contract used as the quoteAmount denomination
    /// @return quoteAmount Amount of quoteToken received for baseAmount of baseToken
    function getQuoteAtTick(
        int24 tick,
        uint128 baseAmount,
        address baseToken,
        address quoteToken
    ) internal pure returns (uint256 quoteAmount) {
        uint160 sqrtRatioX96 = TickMath.getSqrtRatioAtTick(tick);

        // Calculate quoteAmount with better precision if it doesn't overflow when multiplied by itself
        if (sqrtRatioX96 <= type(uint128).max) {
            uint256 ratioX192 = uint256(sqrtRatioX96) * sqrtRatioX96;
            quoteAmount = baseToken < quoteToken
                ? FullMath.mulDiv(ratioX192, baseAmount, 1 << 192)
                : FullMath.mulDiv(1 << 192, baseAmount, ratioX192);
        } else {
            uint256 ratioX128 = FullMath.mulDiv(sqrtRatioX96, sqrtRatioX96, 1 << 64);
            quoteAmount = baseToken < quoteToken
                ? FullMath.mulDiv(ratioX128, baseAmount, 1 << 128)
                : FullMath.mulDiv(1 << 128, baseAmount, ratioX128);
        }
    }

    /// @notice Given a pool, it returns the number of seconds ago of the oldest stored observation
    /// @param pool Address of Uniswap V3 pool that we want to observe
    /// @return secondsAgo The number of seconds ago of the oldest observation stored for the pool
    function getOldestObservationSecondsAgo(address pool) internal view returns (uint32 secondsAgo) {
        (, , uint16 observationIndex, uint16 observationCardinality, , , ) = IUniswapV3Pool(pool).slot0();
        require(observationCardinality > 0, 'NI');

        (uint32 observationTimestamp, , , bool initialized) = IUniswapV3Pool(pool).observations(
            (observationIndex + 1) % observationCardinality
        );

        // The next index might not be initialized if the cardinality is in the process of increasing
        // In this case the oldest observation is always in index 0
        if (!initialized) {
            (observationTimestamp, , , ) = IUniswapV3Pool(pool).observations(0);
        }

        unchecked {
            secondsAgo = uint32(block.timestamp) - observationTimestamp;
        }
    }

    /// @notice Given a pool, it returns the tick value as of the start of the current block
    /// @param pool Address of Uniswap V3 pool
    /// @return The tick that the pool was in at the start of the current block
    function getBlockStartingTickAndLiquidity(address pool) internal view returns (int24, uint128) {
        (, int24 tick, uint16 observationIndex, uint16 observationCardinality, , , ) = IUniswapV3Pool(pool).slot0();

        // 2 observations are needed to reliably calculate the block starting tick
        require(observationCardinality > 1, 'NEO');

        // If the latest observation occurred in the past, then no tick-changing trades have happened in this block
        // therefore the tick in `slot0` is the same as at the beginning of the current block.
        // We don't need to check if this observation is initialized - it is guaranteed to be.
        (
            uint32 observationTimestamp,
            int56 tickCumulative,
            uint160 secondsPerLiquidityCumulativeX128,

        ) = IUniswapV3Pool(pool).observations(observationIndex);
        if (observationTimestamp != uint32(block.timestamp)) {
            return (tick, IUniswapV3Pool(pool).liquidity());
        }

        uint256 prevIndex = (uint256(observationIndex) + observationCardinality - 1) % observationCardinality;
        (
            uint32 prevObservationTimestamp,
            int56 prevTickCumulative,
            uint160 prevSecondsPerLiquidityCumulativeX128,
            bool prevInitialized
        ) = IUniswapV3Pool(pool).observations(prevIndex);

        require(prevInitialized, 'ONI');

        uint32 delta = observationTimestamp - prevObservationTimestamp;
        tick = int24((tickCumulative - int56(uint56(prevTickCumulative))) / int56(uint56(delta)));
        uint128 liquidity = uint128(
            (uint192(delta) * type(uint160).max) /
                (uint192(secondsPerLiquidityCumulativeX128 - prevSecondsPerLiquidityCumulativeX128) << 32)
        );
        return (tick, liquidity);
    }

    /// @notice Information for calculating a weighted arithmetic mean tick
    struct WeightedTickData {
        int24 tick;
        uint128 weight;
    }

    /// @notice Given an array of ticks and weights, calculates the weighted arithmetic mean tick
    /// @param weightedTickData An array of ticks and weights
    /// @return weightedArithmeticMeanTick The weighted arithmetic mean tick
    /// @dev Each entry of `weightedTickData` should represents ticks from pools with the same underlying pool tokens. If they do not,
    /// extreme care must be taken to ensure that ticks are comparable (including decimal differences).
    /// @dev Note that the weighted arithmetic mean tick corresponds to the weighted geometric mean price.
    function getWeightedArithmeticMeanTick(WeightedTickData[] memory weightedTickData)
        internal
        pure
        returns (int24 weightedArithmeticMeanTick)
    {
        // Accumulates the sum of products between each tick and its weight
        int256 numerator;

        // Accumulates the sum of the weights
        uint256 denominator;

        // Products fit in 152 bits, so it would take an array of length ~2**104 to overflow this logic
        for (uint256 i; i < weightedTickData.length; i++) {
            numerator += weightedTickData[i].tick * int256(uint256(weightedTickData[i].weight));
            denominator += weightedTickData[i].weight;
        }

        weightedArithmeticMeanTick = int24(numerator / int256(denominator));
        // Always round to negative infinity
        if (numerator < 0 && (numerator % int256(denominator) != 0)) weightedArithmeticMeanTick--;
    }

    /// @notice Returns the "synthetic" tick which represents the price of the first entry in `tokens` in terms of the last
    /// @dev Useful for calculating relative prices along routes.
    /// @dev There must be one tick for each pairwise set of tokens.
    /// @param tokens The token contract addresses
    /// @param ticks The ticks, representing the price of each token pair in `tokens`
    /// @return syntheticTick The synthetic tick, representing the relative price of the outermost tokens in `tokens`
    function getChainedPrice(address[] memory tokens, int24[] memory ticks)
        internal
        pure
        returns (int256 syntheticTick)
    {
        require(tokens.length - 1 == ticks.length, 'DL');
        for (uint256 i = 1; i <= ticks.length; i++) {
            // check the tokens for address sort order, then accumulate the
            // ticks into the running synthetic tick, ensuring that intermediate tokens "cancel out"
            tokens[i - 1] < tokens[i] ? syntheticTick += ticks[i - 1] : syntheticTick -= ticks[i - 1];
        }
    }
}

// File: src/AMasterchefBase.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { IERC20, SafeERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { Math } from '@openzeppelin/contracts/utils/math/Math.sol';
import { Ownable } from '@openzeppelin/contracts/access/Ownable.sol';
import { APermit } from './APermit.sol';

abstract contract AMasterchefBase is APermit, Ownable {
  using SafeERC20 for IERC20;

  event Add(uint256 indexed pid, uint256 allocPoint, address indexed token);
  event SetRewardDistributor(address indexed caller, address indexed rewardDistributor);
  event Deposit(address indexed user, uint256 indexed pid, uint256 amount);
  event Withdraw(address indexed user, uint256 indexed pid, uint256 amount);
  event Claim(address indexed user, uint256 indexed pid, uint256 amount);
  event EmergencyWithdraw(address indexed user, uint256 indexed pid, uint256 amount);
  event UpdateRewards(address indexed caller, uint256 amount, uint256 newRewardRate, uint256 newPeriodFinish);

  struct UserInfo {
    uint256 amount;
    uint256 rewardDebt;
  }

  struct PoolInfo {
    address token;
    uint32 allocPoint;
    uint64 lastUpdateTime;
    uint256 totalStaked;
    uint256 accRewardPerShare;
    uint256 accUndistributedReward;
  }

  uint256 public constant PRECISION = 1e20;
  uint256 public immutable REWARDS_DURATION;
  address public immutable REWARD_TOKEN;

  uint256 public totalAllocPoint;
  uint256 public totalClaimedRewards;
  uint256 public rewardRate;
  uint256 public periodFinish;

  PoolInfo[] public poolInfo;
  mapping(uint256 => mapping(address => UserInfo)) public userInfo;
  mapping(address => bool) private poolToken;

  constructor(address rewardToken_, uint256 rewardsDuration_) {
    REWARD_TOKEN = rewardToken_;
    REWARDS_DURATION = rewardsDuration_;
    periodFinish = block.timestamp + rewardsDuration_;
  }

  function add(uint32 allocPoint, address token) external onlyOwner {
    require(!poolToken[token], 'Masterchef: Token already added');
    require(token != REWARD_TOKEN, 'Masterchef: Staking reward token not supported');
    require(allocPoint != 0, 'Masterchef: Allocation must be non zero');

    if (totalAllocPoint != 0) _massUpdatePools();

    totalAllocPoint += allocPoint;

    poolInfo.push(
      PoolInfo({
        token: token,
        allocPoint: allocPoint,
        lastUpdateTime: uint64(block.timestamp),
        totalStaked: 0,
        accRewardPerShare: 0,
        accUndistributedReward: 0
      })
    );

    poolToken[address(token)] = true;

    emit Add(poolInfo.length - 1, allocPoint, token);
  }

  function deposit(uint256 pid, uint256 amount) public virtual {
    PoolInfo storage pool = poolInfo[pid];
    UserInfo storage user = userInfo[pid][msg.sender];
    _updatePool(pool);

    /// @dev Undistributed rewards to this pool are divided equally between all active pools.
    if (pool.totalStaked == 0) {
      _updateUndistributedRewards(pool.accUndistributedReward / PRECISION);
      pool.accUndistributedReward = 0;
    } else {
      _safeClaimRewards(pid, _getUserPendingReward(user.amount, user.rewardDebt, pool.accRewardPerShare));
    }

    _transferAmountIn(pool.token, amount);
    user.amount += amount;
    user.rewardDebt = (user.amount * pool.accRewardPerShare) / PRECISION;
    pool.totalStaked += amount;

    emit Deposit(msg.sender, pid, amount);
  }

  function depositWithPermit(uint256 pid, uint256 amount, PermitParameters memory _permitParams) external {
    _permitToken(_permitParams);
    deposit(pid, amount);
  }

  function withdraw(uint256 pid, uint256 amount) public {
    PoolInfo storage pool = poolInfo[pid];
    UserInfo storage user = userInfo[pid][msg.sender];
    _updatePool(pool);

    amount = Math.min(user.amount, amount);

    _safeClaimRewards(pid, _getUserPendingReward(user.amount, user.rewardDebt, pool.accRewardPerShare));

    user.amount -= amount;
    user.rewardDebt = (user.amount * pool.accRewardPerShare) / PRECISION;
    pool.totalStaked -= amount;
    _transferAmountOut(pool.token, amount);

    emit Withdraw(msg.sender, pid, amount);
  }

  /// @notice Caution this will clear any pending rewards without claiming them.
  function emergencyWithdraw(uint256 pid) external {
    PoolInfo storage pool = poolInfo[pid];
    UserInfo storage user = userInfo[pid][msg.sender];

    uint256 _amount = user.amount;
    user.amount = 0;
    user.rewardDebt = 0;
    pool.totalStaked -= _amount;

    IERC20(pool.token).safeTransfer(address(msg.sender), _amount);
    emit EmergencyWithdraw(msg.sender, pid, _amount);
    // No mass update don't update pending rewards
  }

  /// @notice Adds rewards to the pool and updates the reward rate.
  /// Must add and evenly distribute rewards through the rewardsDuration.
  function updateRewards(uint256 amount) external virtual onlyOwner {
    require(totalAllocPoint != 0, 'Masterchef: Must initiate a pool before updating rewards');
    IERC20(REWARD_TOKEN).safeTransferFrom(msg.sender, address(this), amount);

    _updateUndistributedRewards(amount);
    emit UpdateRewards(msg.sender, amount, rewardRate, periodFinish);
  }

  function poolLength() external view returns (uint256) {
    return poolInfo.length;
  }

  function pendingReward(uint256 pid, address user_) external view returns (uint256) {
    PoolInfo storage pool = poolInfo[pid];
    UserInfo storage user = userInfo[pid][user_];

    if (user.amount == 0) return 0;

    uint256 accRewardPerShare = pool.accRewardPerShare +
      _getPoolRewardsSinceLastUpdate(pool.lastUpdateTime, pool.allocPoint) /
      pool.totalStaked;

    return
      Math.min(
        IERC20(REWARD_TOKEN).balanceOf(address(this)),
        _getUserPendingReward(user.amount, user.rewardDebt, accRewardPerShare)
      );
  }

  function _updateUndistributedRewards(uint256 _amount) internal {
    // Updates pool to account for the previous rewardRate.
    _massUpdatePools();

    uint256 amount = _amount * PRECISION;
    if (block.timestamp < periodFinish) {
      uint256 undistributedRewards = rewardRate * (periodFinish - block.timestamp);
      amount += undistributedRewards;
    }
    rewardRate = amount / REWARDS_DURATION;
    periodFinish = block.timestamp + REWARDS_DURATION;
  }

  // Increases accRewardPerShare and accUndistributedReward since last update.
  // Every time there is an update on *stake amount* we should update THE pool.
  function _updatePool(PoolInfo storage pool) internal {
    uint256 poolRewards = _getPoolRewardsSinceLastUpdate(pool.lastUpdateTime, pool.allocPoint);

    if (poolRewards != 0) {
      if (pool.totalStaked == 0) {
        pool.accUndistributedReward += poolRewards;
      } else {
        pool.accRewardPerShare += poolRewards / pool.totalStaked;
      }
    }

    pool.lastUpdateTime = uint64(block.timestamp);
  }

  /// @notice Increases accRewardPerShare and accUndistributedReward for all pools since last update up to block.timestamp.
  /// Every time there is an update on *rewardRate* or *totalAllocPoint* we should update ALL pools.
  function _massUpdatePools() internal {
    uint256 length = poolInfo.length;
    for (uint256 pid = 0; pid < length; ++pid) {
      _updatePool(poolInfo[pid]);
    }
  }

  function _safeClaimRewards(uint256 _pid, uint256 _amount) internal {
    if (_amount == 0) return;
    uint256 _claimable = Math.min(_amount, IERC20(REWARD_TOKEN).balanceOf(address(this)));
    totalClaimedRewards += _claimable;
    IERC20(REWARD_TOKEN).safeTransfer(msg.sender, _claimable);
    emit Claim(msg.sender, _pid, _claimable);
  }

  function _transferAmountIn(address _token, uint256 _amount) internal {
    if (_amount != 0) IERC20(_token).safeTransferFrom(msg.sender, address(this), _amount);
  }

  function _transferAmountOut(address _token, uint256 _amount) internal {
    if (_amount != 0) IERC20(_token).safeTransfer(msg.sender, _amount);
  }

  // @notice Returns the total rewards allocated to a pool since last update.
  function _getPoolRewardsSinceLastUpdate(
    uint256 _poolLastUpdateTime,
    uint256 _poolAllocPoint
  ) internal view returns (uint256 _poolRewards) {
    // If _updatePool has not been called since periodFinish
    if (_poolLastUpdateTime > periodFinish) return 0;

    // If reward is not updated for longer than rewardsDuration periodFinish will be < than block.timestamp
    uint256 lastTimeRewardApplicable = Math.min(block.timestamp, periodFinish);

    return ((lastTimeRewardApplicable - _poolLastUpdateTime) * rewardRate * _poolAllocPoint) / totalAllocPoint;
  }

  function _getUserPendingReward(
    uint256 _userAmount,
    uint256 _userDebt,
    uint256 _poolAccRewardPerShare
  ) internal pure returns (uint256 _reward) {
    return (_userAmount * _poolAccRewardPerShare) / PRECISION - _userDebt;
  }
}

// File: src/APermit.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { IERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { IERC20Permit } from '@openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol';

abstract contract APermit {
  struct PermitParameters {
    address token;
    address owner;
    address spender;
    uint256 value;
    uint256 deadline;
    uint8 v;
    bytes32 r;
    bytes32 s;
  }

  function _permitToken(PermitParameters memory _permitParams) internal {
    if (IERC20(_permitParams.token).allowance(_permitParams.owner, _permitParams.spender) < _permitParams.value) {
      IERC20Permit(_permitParams.token).permit(
        _permitParams.owner,
        _permitParams.spender,
        _permitParams.value,
        _permitParams.deadline,
        _permitParams.v,
        _permitParams.r,
        _permitParams.s
      );
    }
  }

  function _permitTokens(PermitParameters memory _permitParams0, PermitParameters memory _permitParams1) internal {
    _permitToken(_permitParams0);
    _permitToken(_permitParams1);
  }
}

// File: src/BaseToken.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import { ERC20, ERC20Permit } from '@openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol';
import { Ownable } from '@openzeppelin/contracts/access/Ownable.sol';

contract BaseToken is ERC20Permit, Ownable {
  constructor(string memory name_, string memory symbol_) ERC20(name_, symbol_) ERC20Permit(name_) {}

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

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

// File: src/Exit10.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import { OracleLibrary } from '@uniswap/v3-periphery/contracts/libraries/OracleLibrary.sol';
import { IERC20, SafeERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { Math } from '@openzeppelin/contracts/utils/math/Math.sol';
import { ERC20 } from '@openzeppelin/contracts/token/ERC20/ERC20.sol';
import { INPM } from './interfaces/INonfungiblePositionManager.sol';
import { IUniswapV3Pool } from './interfaces/IUniswapV3Pool.sol';
import { INFT } from './interfaces/INFT.sol';
import { BaseToken } from './BaseToken.sol';
import { FeeSplitter } from './FeeSplitter.sol';
import { IWETH9, UniswapBase } from './UniswapBase.sol';
import { MasterchefExit } from './MasterchefExit.sol';
import { STOToken } from './STOToken.sol';
import { APermit } from './APermit.sol';
import { ILido } from './interfaces/ILido.sol';

contract Exit10 is UniswapBase, APermit {
  using SafeERC20 for IERC20;
  using Math for uint256;

  struct DeployParams {
    address NFT;
    address STO;
    address BOOT;
    address BLP;
    address EXIT;
    address masterchef; // EXIT/USDC Stakers
    address feeSplitter; // Distribution to STO + BOOT and BLP stakers
    address beneficiary; // Address to receive fees if pool goes back into range after Exit10
    address lido;
    uint256 bootstrapStart;
    uint256 bootstrapDuration;
    uint256 bootstrapCap;
    uint256 accrualParameter; // The number of seconds it takes to accrue 50% of the cap, represented as an 18 digit fixed-point number.
  }

  struct BondData {
    uint256 bondAmount;
    uint256 claimedBLP;
    uint64 startTime;
    uint64 endTime;
    BondStatus status;
  }

  enum BondStatus {
    nonExistent,
    active,
    cancelled,
    converted
  }

  uint256 private pendingBucket;
  uint256 private reserveBucket;
  uint256 private bootstrapBucket;
  uint256 public bootstrapBucketFinal;
  uint256 public exitBucketBootstrapBucketFinal;

  // EXIT TOKEN
  uint256 public exitTokenSupplyFinal;
  uint256 public exitTokenRewardsFinal;

  // BOOT TOKEN
  uint256 public bootstrapRewardsPlusRefund;

  // STO TOKEN
  uint256 public teamPlusBackersRewards;

  bool public isBootstrapCapReached;
  bool public inExitMode;
  bool private hasUpdatedRewards;

  mapping(uint256 => BondData) private idToBondData;

  uint256 public constant TOKEN_MULTIPLIER = 1e8;
  uint256 public constant MAX_EXIT_SUPPLY = 100_000_000 ether;
  uint128 private constant MAX_UINT_128 = type(uint128).max;
  uint256 private constant MAX_UINT_256 = type(uint256).max;
  uint256 private constant DEADLINE = 1e10;

  BaseToken public immutable STO;
  BaseToken public immutable BOOT;
  BaseToken public immutable BLP;
  BaseToken public immutable EXIT;
  INFT public immutable NFT;

  address public immutable LIDO;
  address public immutable BENEFICIARY;
  address public immutable MASTERCHEF;
  address public immutable FEE_SPLITTER;

  uint256 public immutable BOOTSTRAP_START;
  uint256 public immutable BOOTSTRAP_FINISH;
  uint256 public immutable BOOTSTRAP_LIQUIDITY_CAP;
  uint256 public immutable ACCRUAL_PARAMETER;

  event BootstrapLock(
    address indexed recipient,
    uint256 lockAmount,
    uint256 amountAdded0,
    uint256 amountAdded1,
    uint256 bootTokensMinted
  );
  event CreateBond(
    address indexed recipient,
    uint256 bondID,
    uint256 bondAmount,
    uint256 amountAdded0,
    uint256 amountAdded1
  );
  event CancelBond(address indexed caller, uint256 bondID, uint256 amountReturned0, uint256 amountReturned1);
  event ConvertBond(address indexed caller, uint256 bondID, uint256 bondAmount, uint256 accrued, uint256 blpClaimed);
  event Redeem(address indexed caller, uint256 burnedBLP, uint256 amountReturned0, uint256 amountReturned1);
  event Exit(
    address indexed caller,
    uint256 time,
    uint256 bootstrapRefund,
    uint256 bootstrapRewards,
    uint256 teamPlusBackersRewards,
    uint256 exitTokenRewards
  );
  event BootClaim(address indexed caller, address indexed token, uint256 amountBurned, uint256 amountClaimed);
  event StoClaim(address indexed caller, address indexed token, uint256 amountBurned, uint256 amountClaimed);
  event ExitClaim(
    address indexed caller,
    address indexed token,
    uint256 amountBurned,
    uint256 liquidityClaimed,
    uint256 feesClaimed,
    uint256 stakedEthClaimed
  );
  event ClaimAndDistributeFees(address indexed caller, uint256 amountClaimed0, uint256 amountClaimed1);
  event StakeEth(address indexed caller, uint256 amountStaked, uint256 sharesReceived);

  constructor(BaseDeployParams memory baseParams_, DeployParams memory params_) UniswapBase(baseParams_) {
    STO = STOToken(params_.STO);
    BOOT = BaseToken(params_.BOOT);
    BLP = BaseToken(params_.BLP);
    EXIT = BaseToken(params_.EXIT);
    NFT = INFT(params_.NFT);

    MASTERCHEF = params_.masterchef;
    FEE_SPLITTER = params_.feeSplitter;
    BENEFICIARY = params_.beneficiary;
    LIDO = params_.lido;

    BOOTSTRAP_START = params_.bootstrapStart;
    BOOTSTRAP_FINISH = params_.bootstrapDuration + params_.bootstrapStart;
    BOOTSTRAP_LIQUIDITY_CAP = params_.bootstrapCap;
    ACCRUAL_PARAMETER = params_.accrualParameter;

    IERC20(IUniswapV3Pool(POOL).token0()).approve(NPM, MAX_UINT_256);
    IERC20(IUniswapV3Pool(POOL).token1()).approve(NPM, MAX_UINT_256);
    IERC20(IUniswapV3Pool(POOL).token0()).approve(FEE_SPLITTER, MAX_UINT_256);
    IERC20(IUniswapV3Pool(POOL).token1()).approve(FEE_SPLITTER, MAX_UINT_256);
  }

  receive() external payable {}

  function bootstrapLock(
    AddLiquidity memory params
  ) public payable returns (uint256 tokenId, uint128 liquidityAdded, uint256 amountAdded0, uint256 amountAdded1) {
    _requireNoExitMode();
    require(block.timestamp >= BOOTSTRAP_START, 'EXIT10: Bootstrap not started');
    require(_isBootstrapOngoing(), 'EXIT10: Bootstrap ended');
    require(!isBootstrapCapReached, 'EXIT10: Bootstrap cap reached');

    _depositTokens(params.amount0Desired, params.amount1Desired);

    (tokenId, liquidityAdded, amountAdded0, amountAdded1) = _addLiquidity(params);

    bootstrapBucket += liquidityAdded;

    if (BOOTSTRAP_LIQUIDITY_CAP != 0) {
      if (bootstrapBucket > BOOTSTRAP_LIQUIDITY_CAP) {
        uint256 diff;
        unchecked {
          diff = bootstrapBucket - BOOTSTRAP_LIQUIDITY_CAP;
        }
        (uint256 amountRemoved0, uint256 amountRemoved1) = _decreaseLiquidity(
          UniswapBase.RemoveLiquidity({ liquidity: uint128(diff), amount0Min: 0, amount1Min: 0, deadline: DEADLINE })
        );
        (uint256 amountCollected0, uint256 amountCollected1) = _collect(
          address(this),
          uint128(amountRemoved0),
          uint128(amountRemoved1)
        );

        liquidityAdded -= uint128(diff);
        amountAdded0 -= amountCollected0;
        amountAdded1 -= amountCollected1;
        bootstrapBucket = BOOTSTRAP_LIQUIDITY_CAP;
        isBootstrapCapReached = true;
      }
    }

    uint256 mintAmount = liquidityAdded * TOKEN_MULTIPLIER;
    BOOT.mint(params.depositor, mintAmount);

    _safeTransferTokens(params.depositor, params.amount0Desired - amountAdded0, params.amount1Desired - amountAdded1);

    emit BootstrapLock(params.depositor, liquidityAdded, amountAdded0, amountAdded1, mintAmount);
  }

  function createBond(
    AddLiquidity memory params
  ) public payable returns (uint256 bondID, uint128 liquidityAdded, uint256 amountAdded0, uint256 amountAdded1) {
    _requireNoExitMode();
    require(!_isBootstrapOngoing(), 'EXIT10: Bootstrap ongoing');

    claimAndDistributeFees();

    _depositTokens(params.amount0Desired, params.amount1Desired);

    (, liquidityAdded, amountAdded0, amountAdded1) = _addLiquidity(params);

    bondID = NFT.mint(params.depositor);

    BondData memory bondData;
    bondData.bondAmount = liquidityAdded;
    bondData.startTime = uint64(block.timestamp);
    bondData.status = BondStatus.active;
    idToBondData[bondID] = bondData;

    pendingBucket += liquidityAdded;

    _safeTransferTokens(params.depositor, params.amount0Desired - amountAdded0, params.amount1Desired - amountAdded1);

    emit CreateBond(params.depositor, bondID, liquidityAdded, amountAdded0, amountAdded1);
  }

  function stakeEth(uint256 amount) external returns (uint256 share) {
    _requireNoExitMode();
    IWETH9(WETH).withdraw(amount);
    uint256 amountEth = address(this).balance;
    share = ILido(LIDO).submit{ value: amountEth }(BENEFICIARY);
    require(share > 0, 'Exit10: Deposited zero amount');
    emit StakeEth(msg.sender, amountEth, share);
  }

  function bootstrapLockWithPermit(
    AddLiquidity memory params,
    PermitParameters memory permitParams0,
    PermitParameters memory permitParams1
  ) external payable returns (uint256 tokenId, uint128 liquidityAdded, uint256 amountAdded0, uint256 amountAdded1) {
    _permitTokens(permitParams0, permitParams1);
    return bootstrapLock(params);
  }

  function createBondWithPermit(
    AddLiquidity memory params,
    PermitParameters memory permitParams0,
    PermitParameters memory permitParams1
  ) external payable returns (uint256 bondID, uint128 liquidityAdded, uint256 amountAdded0, uint256 amountAdded1) {
    _permitTokens(permitParams0, permitParams1);
    return createBond(params);
  }

  function cancelBond(
    uint256 bondID,
    RemoveLiquidity memory params
  ) external returns (uint256 amountRemoved0, uint256 amountRemoved1) {
    _requireCallerOwnsBond(bondID);
    BondData memory bond = idToBondData[bondID];
    _requireActiveStatus(bond.status);

    claimAndDistributeFees();

    params.liquidity = uint128(bond.bondAmount);
    idToBondData[bondID].status = BondStatus.cancelled;
    idToBondData[bondID].endTime = uint64(block.timestamp);

    (amountRemoved0, amountRemoved1) = _decreaseLiquidity(params);
    (uint256 amountCollected0, uint256 amountCollected1) = _collect(
      msg.sender,
      uint128(amountRemoved0),
      uint128(amountRemoved1)
    );

    pendingBucket -= params.liquidity;

    emit CancelBond(msg.sender, bondID, amountCollected0, amountCollected1);
  }

  function convertBond(uint256 bondID, RemoveLiquidity memory params) external returns (uint256 blpTokenAmount) {
    _requireNoExitMode();
    _requireCallerOwnsBond(bondID);
    BondData memory bond = idToBondData[bondID];
    _requireActiveStatus(bond.status);

    claimAndDistributeFees();

    params.liquidity = uint128(bond.bondAmount);
    uint256 accruedLiquidity = _getAccruedLiquidity(bond);
    blpTokenAmount = accruedLiquidity * TOKEN_MULTIPLIER;

    idToBondData[bondID].status = BondStatus.converted;
    idToBondData[bondID].endTime = uint64(block.timestamp);
    idToBondData[bondID].claimedBLP = blpTokenAmount;

    pendingBucket -= params.liquidity;
    reserveBucket += accruedLiquidity;

    BLP.mint(msg.sender, blpTokenAmount);

    emit ConvertBond(msg.sender, bondID, bond.bondAmount, accruedLiquidity, blpTokenAmount);
  }

  function redeem(RemoveLiquidity memory params) external returns (uint256 amountRemoved0, uint256 amountRemoved1) {
    claimAndDistributeFees();

    reserveBucket -= params.liquidity;

    uint256 amountToBurn = params.liquidity * TOKEN_MULTIPLIER;
    BLP.burn(msg.sender, amountToBurn);

    (amountRemoved0, amountRemoved1) = _decreaseLiquidity(params);
    (uint256 amountCollected0, uint256 amountCollected1) = _collect(
      msg.sender,
      uint128(amountRemoved0),
      uint128(amountRemoved1)
    );

    emit Redeem(msg.sender, amountToBurn, amountCollected0, amountCollected1);
  }

  function exit10() external {
    _requireNoExitMode();
    _requireOutOfTickRange();

    claimAndDistributeFees();

    inExitMode = true;

    exitTokenSupplyFinal = EXIT.totalSupply();
    exitBucketBootstrapBucketFinal = _liquidityAmount() - (pendingBucket + reserveBucket);
    bootstrapBucketFinal = bootstrapBucket;
    bootstrapBucket = 0;

    RemoveLiquidity memory rmParams = RemoveLiquidity({
      liquidity: uint128(exitBucketBootstrapBucketFinal),
      amount0Min: 0,
      amount1Min: 0,
      deadline: DEADLINE
    });

    uint256 exitBucketBootstrapBucketRewards;

    if (TOKEN_OUT < TOKEN_IN) {
      (exitBucketBootstrapBucketRewards, ) = _decreaseLiquidity(rmParams);
      (exitBucketBootstrapBucketRewards, ) = _collect(address(this), uint128(exitBucketBootstrapBucketRewards), 0);
    } else {
      (, exitBucketBootstrapBucketRewards) = _decreaseLiquidity(rmParams);
      (, exitBucketBootstrapBucketRewards) = _collect(address(this), 0, uint128(exitBucketBootstrapBucketRewards));
    }

    // Total initial deposits that needs to be returned to bootstrappers
    uint256 bootstrapRefund = exitBucketBootstrapBucketFinal != 0
      ? (bootstrapBucketFinal * exitBucketBootstrapBucketRewards) / exitBucketBootstrapBucketFinal
      : 0;

    (bootstrapRewardsPlusRefund, teamPlusBackersRewards, exitTokenRewardsFinal) = _calculateFinalShares(
      bootstrapRefund,
      exitBucketBootstrapBucketRewards,
      bootstrapBucketFinal,
      exitTokenSupplyFinal
    );

    emit Exit(
      msg.sender,
      block.timestamp,
      bootstrapRefund,
      bootstrapRewardsPlusRefund - bootstrapRefund,
      teamPlusBackersRewards,
      exitTokenRewardsFinal
    );
  }

  function bootstrapClaim() external returns (uint256 claim) {
    _requireExitMode();
    BaseToken boot = BOOT;
    uint256 bootBalance = boot.balanceOf(msg.sender);

    claim = _getClaimableAmount(bootBalance / TOKEN_MULTIPLIER, bootstrapBucketFinal, bootstrapRewardsPlusRefund);

    boot.burn(msg.sender, bootBalance);
    _safeTransferToken(TOKEN_OUT, msg.sender, claim);

    emit BootClaim(msg.sender, address(BOOT), bootBalance, claim);
  }

  function stoClaim() external returns (uint256 claim) {
    _requireExitMode();
    BaseToken sto = STO;
    uint256 stoBalance = sto.balanceOf(msg.sender);

    claim = _getClaimableAmount(stoBalance, STOToken(address(sto)).MAX_SUPPLY(), teamPlusBackersRewards);

    sto.burn(msg.sender, stoBalance);
    _safeTransferToken(TOKEN_OUT, msg.sender, claim);

    emit StoClaim(msg.sender, address(STO), stoBalance, claim);
  }

  function exitClaim() external returns (uint256 claimedLiquidity, uint256 claimedFees, uint256 claimedStakedEth) {
    _requireExitMode();
    BaseToken exit = EXIT;
    uint256 exitBalance = exit.balanceOf(msg.sender);
    uint256 exitTotalSupply = exit.totalSupply();

    claimedLiquidity = _getClaimableAmount(exitBalance, exitTokenSupplyFinal, exitTokenRewardsFinal);
    claimedFees = _getClaimableAmount(exitBalance, exitTotalSupply, IERC20(TOKEN_IN).balanceOf(address(this)));

    uint256 shares;
    if (LIDO != address(0))
      shares = _getClaimableAmount(exitBalance, exitTotalSupply, ILido(LIDO).sharesOf(address(this)));

    exit.burn(msg.sender, exitBalance);

    _safeTransferToken(TOKEN_OUT, msg.sender, claimedLiquidity);
    _safeTransferToken(TOKEN_IN, msg.sender, claimedFees);
    if (shares != 0) claimedStakedEth = ILido(LIDO).transferShares(msg.sender, shares);

    emit ExitClaim(msg.sender, address(exit), exitBalance, claimedLiquidity, claimedFees, claimedStakedEth);
  }

  function getBondData(
    uint256 bondID
  ) external view returns (uint256 bondAmount, uint256 claimedBLP, uint64 startTime, uint64 endTime, uint8 status) {
    BondData memory bond = idToBondData[bondID];
    return (bond.bondAmount, bond.claimedBLP, bond.startTime, bond.endTime, uint8(bond.status));
  }

  function getBuckets() external view returns (uint256 pending, uint256 reserve, uint256 exit, uint256 bootstrap) {
    pending = pendingBucket;
    reserve = reserveBucket;
    bootstrap = bootstrapBucket;
    exit = _exitBucket();
  }

  function getAccruedAmount(uint256 bondID) external view returns (uint256) {
    BondData memory bond = idToBondData[bondID];

    if (bond.status != BondStatus.active) {
      return 0;
    }

    return _getAccruedLiquidity(bond);
  }

  function claimAndDistributeFees() public {
    (uint256 amountCollected0, uint256 amountCollected1) = _collect(address(this), MAX_UINT_128, MAX_UINT_128);

    if (amountCollected0 + amountCollected1 == 0) return;

    if (!inExitMode) {
      uint256 amountTokenOut;
      uint256 amountTokenIn;

      if (TOKEN_OUT < TOKEN_IN) {
        (amountTokenOut, amountTokenIn) = (amountCollected0, amountCollected1);
      } else {
        (amountTokenOut, amountTokenIn) = (amountCollected1, amountCollected0);
      }

      FeeSplitter(FEE_SPLITTER).collectFees(amountTokenOut, amountTokenIn);
    } else {
      // In case liquidity from Pending + Reserve buckets goes back in range after Exit10
      _safeTransferTokens(BENEFICIARY, amountCollected0, amountCollected1);
    }

    emit ClaimAndDistributeFees(msg.sender, amountCollected0, amountCollected1);
  }

  function updateRewards(uint256 amountTokenIn) external {
    require(msg.sender == FEE_SPLITTER, 'Exit10: Caller not authorized.');
    if (inExitMode) return;
    // For every 1 ETH acquired in fees we mint 1000 EXIT tokens
    uint256 mintAmount = amountTokenIn * 1000;
    mintAmount = _mintExitCapped(MASTERCHEF, mintAmount);
    MasterchefExit(MASTERCHEF).updateRewards(mintAmount);
  }

  function _getClaimableAmount(
    uint256 _shares,
    uint256 _totalSupply,
    uint256 _totalAssets
  ) internal pure returns (uint256 _claimable) {
    require(_shares != 0, 'EXIT10: Amount must be != 0');
    _claimable = _shares.mulDiv(_totalAssets, _totalSupply, Math.Rounding.Down);
  }

  function _depositTokens(uint256 _amount0, uint256 _amount1) internal {
    IERC20(POOL.token0()).safeTransferFrom(msg.sender, address(this), _amount0);
    IERC20(POOL.token1()).safeTransferFrom(msg.sender, address(this), _amount1);
  }

  function _safeTransferTokens(address _recipient, uint256 _amount0, uint256 _amount1) internal {
    _safeTransferToken(POOL.token0(), _recipient, _amount0);
    _safeTransferToken(POOL.token1(), _recipient, _amount1);
  }

  function _safeTransferToken(address _token, address _recipient, uint256 _amount) internal {
    if (_amount != 0) IERC20(_token).safeTransfer(_recipient, _amount);
  }

  function _mintExitCapped(address recipient, uint256 amount) internal returns (uint256 mintAmount) {
    uint256 newSupply = EXIT.totalSupply() + amount;
    mintAmount = newSupply > MAX_EXIT_SUPPLY ? MAX_EXIT_SUPPLY - EXIT.totalSupply() : amount;
    if (mintAmount != 0) EXIT.mint(recipient, mintAmount);
  }

  function _exitBucket() internal view returns (uint256 _exitAmount) {
    if (positionId == 0) return 0;
    _exitAmount = inExitMode ? 0 : _liquidityAmount() - (pendingBucket + reserveBucket + bootstrapBucket);
  }

  function _liquidityAmount() internal view returns (uint128 _liquidity) {
    if (positionId != 0) (, , , , , , , _liquidity, , , , ) = INPM(NPM).positions(positionId);
  }

  function _currentTick() internal view returns (int24 _tick) {
    (, _tick, , , , , ) = POOL.slot0();
  }

  function _getAccruedLiquidity(BondData memory _params) internal view returns (uint256 accruedAmount) {
    uint256 bondDuration = block.timestamp - _params.startTime;
    accruedAmount = (_params.bondAmount * bondDuration) / (bondDuration + ACCRUAL_PARAMETER);
  }

  function _isBootstrapOngoing() internal view returns (bool) {
    return (block.timestamp < BOOTSTRAP_FINISH);
  }

  function _requireExitMode() internal view {
    require(inExitMode, 'EXIT10: Not in Exit mode');
  }

  function _requireNoExitMode() internal view {
    require(!inExitMode, 'EXIT10: In Exit mode');
  }

  function _requireOutOfTickRange() internal view {
    (int24 blockStartTick, ) = OracleLibrary.getBlockStartingTickAndLiquidity(address(POOL));
    int24 currentTick = _currentTick();
    int24 tickDiff = blockStartTick > currentTick ? blockStartTick - currentTick : currentTick - blockStartTick;
    bool limit = (tickDiff < 100); // 100 ticks is about 1% in price difference
    if (TOKEN_IN > TOKEN_OUT) {
      require(currentTick <= TICK_LOWER && limit, 'EXIT10: Not out of tick range');
    } else {
      require(currentTick >= TICK_UPPER && limit, 'EXIT10: Not out of tick range');
    }
  }

  function _requireCallerOwnsBond(uint256 _bondID) internal view {
    require(msg.sender == NFT.ownerOf(_bondID), 'EXIT10: Caller must own the bond');
  }

  function _requireActiveStatus(BondStatus _status) internal pure {
    require(_status == BondStatus.active, 'EXIT10: Bond must be active');
  }

  function _calculateFinalShares(
    uint256 _refund,
    uint256 _totalRewards,
    uint256 _bootstrapBucket,
    uint256 _exitSupply
  ) internal pure returns (uint256 _bootRewards, uint256 _stoRewards, uint256 _exitRewards) {
    uint256 exitBucketMinusRefund = _totalRewards - _refund;
    uint256 tenPercent = exitBucketMinusRefund / 10;

    if (_bootstrapBucket != 0) {
      // Initial deposit plus 10% of the Exit Bucket
      _bootRewards = _refund + tenPercent;
    }
    // 20% of the ExitLiquidity
    _stoRewards = tenPercent << 1;

    if (_exitSupply != 0) {
      // 70% Exit Token holders
      _exitRewards = _totalRewards - (_bootRewards + _stoRewards);
    } else {
      _stoRewards = _totalRewards - _bootRewards;
    }
  }
}

// File: src/FeeSplitter.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import { IERC20, SafeERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { Math } from '@openzeppelin/contracts/utils/math/Math.sol';
import { Ownable } from '@openzeppelin/contracts/access/Ownable.sol';
import { IUniswapV3Pool } from './interfaces/IUniswapV3Pool.sol';
import { ISwapper } from './interfaces/ISwapper.sol';
import { Masterchef } from './Masterchef.sol';
import { Exit10 } from './Exit10.sol';

contract FeeSplitter is Ownable {
  using SafeERC20 for IERC20;

  uint16 constant SLIPPAGE = 10; //0.1%
  uint32 constant ORACLE_SECONDS = 60;
  uint256 constant MAX_UINT_256 = type(uint256).max;

  address immutable MASTERCHEF; // STO - BOOT Stakers
  address immutable SWAPPER;
  address payable public exit10;

  event SetExit10(address indexed caller, address indexed exit10);
  event CollectFees(uint256 amountTokenOut, uint256 amountTokenIn);
  event UpdateFees(address indexed caller, uint256 amountExchangedIn, uint256 rewardsMasterchef, uint256 rewardsExit10);
  event Swap(uint256 amountIn, uint256 amountOut);

  constructor(address masterchef_, address swapper_) {
    MASTERCHEF = masterchef_;
    SWAPPER = swapper_;
  }

  modifier onlyAuthorized() {
    require(msg.sender == exit10, 'FeeSplitter: Caller not authorized');
    _;
  }

  function setExit10(address payable exit10_) external onlyOwner {
    exit10 = exit10_;
    IERC20(Exit10(exit10).TOKEN_OUT()).approve(SWAPPER, MAX_UINT_256);
    IERC20(Exit10(exit10).TOKEN_IN()).approve(MASTERCHEF, MAX_UINT_256);
    renounceOwnership();

    emit SetExit10(msg.sender, exit10);
  }

  function collectFees(uint256 amountTokenOut, uint256 amountTokenIn) external onlyAuthorized {
    if (amountTokenOut != 0) {
      IERC20(Exit10(exit10).TOKEN_OUT()).safeTransferFrom(exit10, address(this), amountTokenOut);
    }
    if (amountTokenIn != 0) {
      IERC20(Exit10(exit10).TOKEN_IN()).safeTransferFrom(exit10, address(this), amountTokenIn);
    }

    emit CollectFees(amountTokenOut, amountTokenIn);
  }

  function updateFees(uint256 swapAmountOut) external returns (uint256 totalExchangedIn) {
    uint256 balanceTokenOut = IERC20(Exit10(exit10).TOKEN_OUT()).balanceOf(address(this));

    swapAmountOut = Math.min(swapAmountOut, balanceTokenOut);
    if (swapAmountOut != 0) {
      totalExchangedIn = _swap(swapAmountOut);
    }

    uint256 balanceTokenIn = IERC20(Exit10(exit10).TOKEN_IN()).balanceOf(address(this));

    uint256 mcTokenIn = (balanceTokenIn << 1) / 10; // 20%
    uint256 exit10TokenIn = balanceTokenIn - mcTokenIn; // 80%

    if (mcTokenIn != 0) {
      Masterchef(MASTERCHEF).updateRewards(mcTokenIn);
    }
    if (exit10TokenIn != 0) {
      // Invest tokenIn and send it to Exit10
      // For now just send it to Exit10 as tokenIn
      IERC20(Exit10(exit10).TOKEN_IN()).safeTransfer(exit10, exit10TokenIn);
      Exit10(exit10).updateRewards(exit10TokenIn);
    }

    emit UpdateFees(msg.sender, totalExchangedIn, mcTokenIn, exit10TokenIn);
  }

  function _swap(uint256 _amount) internal returns (uint256 _amountAcquired) {
    ISwapper.SwapParameters memory params = ISwapper.SwapParameters({
      recipient: address(this),
      tokenIn: Exit10(exit10).TOKEN_OUT(), // TOKEN_OUT is the sell token going into the swap
      tokenOut: Exit10(exit10).TOKEN_IN(), // TOKEN_IN is the buy token going out of the swap
      fee: Exit10(exit10).FEE(),
      amountIn: _amount,
      slippage: SLIPPAGE,
      oracleSeconds: ORACLE_SECONDS
    });

    _amountAcquired = ISwapper(SWAPPER).swap(params);

    emit Swap(_amount, _amountAcquired);
  }
}

// File: src/Masterchef.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { AMasterchefBase } from './AMasterchefBase.sol';
import { IRewardDistributor } from './interfaces/IRewardDistributor.sol';

contract Masterchef is AMasterchefBase {
  constructor(address rewardToken_, uint256 rewardsDuration_) AMasterchefBase(rewardToken_, rewardsDuration_) {}

  function withdraw(uint256 pid, uint256 amount, uint256 swapAmountOut) external {
    withdraw(pid, amount);
    IRewardDistributor(owner()).updateFees(swapAmountOut);
  }
}

// File: src/MasterchefExit.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { IERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { AMasterchefBase } from './AMasterchefBase.sol';

contract MasterchefExit is AMasterchefBase {
  constructor(address rewardToken_, uint256 rewardsDuration_) AMasterchefBase(rewardToken_, rewardsDuration_) {}

  event UpdateRewards(address indexed caller, uint256 amount);

  function updateRewards(uint256 amount) external override onlyOwner {
    require(totalAllocPoint != 0, 'Masterchef: Must initiate a pool before updating rewards');
    require(IERC20(REWARD_TOKEN).balanceOf(address(this)) >= amount, 'MasterchefExit: Token balance not sufficient');
    _updateUndistributedRewards(amount);
    emit UpdateRewards(msg.sender, amount, rewardRate, periodFinish);
  }
}

// File: src/MerkleDistributor.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;
import { IERC20, SafeERC20 } from '@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol';
import { MerkleProof } from '@openzeppelin/contracts/utils/cryptography/MerkleProof.sol';
import { IMerkleDistributor } from './interfaces/IMerkleDistributor.sol';

error AlreadyClaimed();
error InvalidProof();

contract MerkleDistributor is IMerkleDistributor {
  using SafeERC20 for IERC20;

  address public immutable override token;
  bytes32 public immutable override merkleRoot;

  // This is a packed array of booleans.
  mapping(uint256 => uint256) private claimedBitMap;

  constructor(address token_, bytes32 merkleRoot_) {
    token = token_;
    merkleRoot = merkleRoot_;
  }

  function isClaimed(uint256 index) public view override returns (bool) {
    uint256 claimedWordIndex = index / 256;
    uint256 claimedBitIndex = index % 256;
    uint256 claimedWord = claimedBitMap[claimedWordIndex];
    uint256 mask = (1 << claimedBitIndex);
    return claimedWord & mask == mask;
  }

  function _setClaimed(uint256 index) internal {
    uint256 claimedWordIndex = index / 256;
    uint256 claimedBitIndex = index % 256;
    claimedBitMap[claimedWordIndex] = claimedBitMap[claimedWordIndex] | (1 << claimedBitIndex);
  }

  function claim(
    uint256 index,
    address account,
    uint256 amount,
    bytes32[] calldata merkleProof
  ) public virtual override {
    if (isClaimed(index)) revert AlreadyClaimed();

    // Verify the merkle proof.
    bytes32 node = keccak256(abi.encodePacked(index, account, amount));
    if (!MerkleProof.verify(merkleProof, merkleRoot, node)) revert InvalidProof();

    // Mark it claimed and send the token.
    _setClaimed(index);
    IERC20(token).safeTransfer(account, amount);

    emit Claimed(index, account, amount);
  }
}

// File: src/STOToken.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import { MerkleDistributor, MerkleProof, AlreadyClaimed, InvalidProof } from './MerkleDistributor.sol';
import { BaseToken } from './BaseToken.sol';

contract STOToken is BaseToken, MerkleDistributor {
  uint256 public constant MAX_SUPPLY = 300_000 ether;

  constructor(bytes32 merkleRoot_) BaseToken('Share Token', 'STO') MerkleDistributor(address(this), merkleRoot_) {}

  function claim(uint256 index, address account, uint256 amount, bytes32[] calldata merkleProof) public override {
    if (isClaimed(index)) revert AlreadyClaimed();

    // Verify the merkle proof.
    bytes32 node = keccak256(abi.encodePacked(index, account, amount));
    if (!MerkleProof.verify(merkleProof, merkleRoot, node)) revert InvalidProof();

    // Mark it claimed and send the token.
    _setClaimed(index);
    _mint(account, amount);

    emit Claimed(index, account, amount);
  }
}

// File: src/UniswapBase.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import { IUniswapV3Factory } from './interfaces/IUniswapV3Factory.sol';
import { IUniswapV3Pool } from './interfaces/IUniswapV3Pool.sol';
import { INPM } from './interfaces/INonfungiblePositionManager.sol';
import { IWETH9 } from './interfaces/IWETH9.sol';

abstract contract UniswapBase {
  struct BaseDeployParams {
    address weth;
    address uniswapFactory;
    address nonfungiblePositionManager;
    address tokenIn;
    address tokenOut;
    uint24 fee;
    int24 tickLower;
    int24 tickUpper;
  }

  struct AddLiquidity {
    address depositor; /// @dev depositor The address which the position will be credited to.
    uint256 amount0Desired;
    uint256 amount1Desired;
    uint256 amount0Min;
    uint256 amount1Min;
    uint256 deadline;
  }

  struct RemoveLiquidity {
    uint128 liquidity;
    uint256 amount0Min;
    uint256 amount1Min;
    uint256 deadline;
  }

  IUniswapV3Factory public immutable FACTORY;
  IUniswapV3Pool public immutable POOL;
  address public immutable WETH;
  address public immutable NPM;
  address public immutable TOKEN_IN;
  address public immutable TOKEN_OUT;
  uint24 public immutable FEE;
  int24 public immutable TICK_LOWER;
  int24 public immutable TICK_UPPER;

  uint256 public positionId;

  constructor(BaseDeployParams memory params) {
    FACTORY = IUniswapV3Factory(params.uniswapFactory);
    NPM = params.nonfungiblePositionManager;
    TOKEN_IN = params.tokenIn;
    TOKEN_OUT = params.tokenOut;
    FEE = params.fee;
    TICK_LOWER = params.tickLower;
    TICK_UPPER = params.tickUpper;
    WETH = params.weth;
    POOL = IUniswapV3Pool(FACTORY.getPool(params.tokenIn, params.tokenOut, params.fee));
  }

  function _addLiquidity(
    AddLiquidity memory _params
  ) internal returns (uint256 _tokenId, uint128 _liquidityAdded, uint256 _amountAdded0, uint256 _amountAdded1) {
    (address token0, address token1) = TOKEN_IN < TOKEN_OUT ? (TOKEN_IN, TOKEN_OUT) : (TOKEN_OUT, TOKEN_IN);

    (_params.amount0Desired, _params.amount1Desired) = (msg.value != 0)
      ? _processEth(token0, token1, _params.amount0Desired, _params.amount1Desired, msg.value)
      : (_params.amount0Desired, _params.amount1Desired);

    if (positionId != 0) {
      (_liquidityAdded, _amountAdded0, _amountAdded1) = INPM(NPM).increaseLiquidity(
        INPM.IncreaseLiquidityParams({
          tokenId: positionId,
          amount0Desired: _params.amount0Desired,
          amount1Desired: _params.amount1Desired,
          amount0Min: _params.amount0Min,
          amount1Min: _params.amount1Min,
          deadline: _params.deadline
        })
      );
      _tokenId = positionId;
    } else {
      (_tokenId, _liquidityAdded, _amountAdded0, _amountAdded1) = INPM(NPM).mint(
        INPM.MintParams({
          token0: token0,
          token1: token1,
          fee: FEE,
          tickLower: TICK_LOWER, //Tick needs to exist (right spacing)
          tickUpper: TICK_UPPER, //Tick needs to exist (right spacing)
          amount0Desired: _params.amount0Desired,
          amount1Desired: _params.amount1Desired,
          amount0Min: _params.amount0Min, // Slippage check
          amount1Min: _params.amount1Min, // Slippage check
          recipient: address(this), // Receiver of ERC721
          deadline: _params.deadline
        })
      );
      positionId = _tokenId;
    }
  }

  function _decreaseLiquidity(
    RemoveLiquidity memory _params
  ) internal returns (uint256 _amountRemoved0, uint256 _amountRemoved1) {
    (_amountRemoved0, _amountRemoved1) = INPM(NPM).decreaseLiquidity(
      INPM.DecreaseLiquidityParams({
        tokenId: positionId,
        liquidity: _params.liquidity,
        amount0Min: _params.amount0Min,
        amount1Min: _params.amount1Min,
        deadline: _params.deadline
      })
    );
  }

  function _collect(
    address _recipient,
    uint128 _amount0Max,
    uint128 _amount1Max
  ) internal returns (uint256 _amountCollected0, uint256 _amountCollected1) {
    if (positionId == 0) return (0, 0);
    (_amountCollected0, _amountCollected1) = INPM(NPM).collect(
      INPM.CollectParams({
        tokenId: positionId,
        recipient: _recipient,
        amount0Max: _amount0Max,
        amount1Max: _amount1Max
      })
    );
  }

  function _processEth(
    address _token0,
    address _token1,
    uint256 _initialAmount0,
    uint256 _initialAmount1,
    uint256 _msgValue
  ) internal returns (uint _amount0, uint _amount1) {
    _amount0 = _initialAmount0;
    _amount1 = _initialAmount1;

    IWETH9(WETH).deposit{ value: _msgValue }();
    if (_token0 == WETH) {
      _amount0 += _msgValue;
    } else if (_token1 == WETH) {
      _amount1 += _msgValue;
    }
  }
}

// File: src/interfaces/ILido.sol



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

interface ILido {
  function submit(address _referral) external payable returns (uint256 shares);

  function sharesOf(address _account) external view returns (uint256);

  function transferShares(address _recipient, uint256 _sharesAmount) external returns (uint256 tokens);
}

// File: src/interfaces/IMerkleDistributor.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.0;

// Allows anyone to claim a token if they exist in a merkle root.
interface IMerkleDistributor {
  // Returns the address of the token distributed by this contract.
  function token() external view returns (address);

  // Returns the merkle root of the merkle tree containing account balances available to claim.
  function merkleRoot() external view returns (bytes32);

  // Returns true if the index has been marked claimed.
  function isClaimed(uint256 index) external view returns (bool);

  // Claim the given amount of the token to the given address. Reverts if the inputs are invalid.
  function claim(uint256 index, address account, uint256 amount, bytes32[] calldata merkleProof) external;

  // This event is triggered whenever a call to #claim succeeds.
  event Claimed(uint256 index, address account, uint256 amount);
}

// File: src/interfaces/INFT.sol



// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.0;
import '@openzeppelin/contracts/token/ERC721/extensions/IERC721Enumerable.sol';

interface INFT is IERC721Enumerable {
  function mint(address _bonder) external returns (uint256);

  function getBondAmount(uint256 _tokenID) external view returns (uint256 amount);

  function getBondStartTime(uint256 _tokenID) external view returns (uint256 startTime);

  function getBondEndTime(uint256 _tokenID) external view returns (uint256 endTime);

  function getBondStatus(uint256 _tokenID) external view returns (uint8 status);
}

// File: src/interfaces/INonfungiblePositionManager.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.0;

interface INPM {
  struct MintParams {
    address token0;
    address token1;
    uint24 fee;
    int24 tickLower;
    int24 tickUpper;
    uint256 amount0Desired;
    uint256 amount1Desired;
    uint256 amount0Min;
    uint256 amount1Min;
    address recipient;
    uint256 deadline;
  }

  struct IncreaseLiquidityParams {
    uint256 tokenId;
    uint256 amount0Desired;
    uint256 amount1Desired;
    uint256 amount0Min;
    uint256 amount1Min;
    uint256 deadline;
  }

  struct CollectParams {
    uint256 tokenId;
    address recipient;
    uint128 amount0Max;
    uint128 amount1Max;
  }

  struct DecreaseLiquidityParams {
    uint256 tokenId;
    uint128 liquidity;
    uint256 amount0Min;
    uint256 amount1Min;
    uint256 deadline;
  }

  function positions(uint256 tokenId)
    external
    view
    returns (
      uint96 nonce,
      address operator,
      address token0,
      address token1,
      uint24 fee,
      int24 tickLower,
      int24 tickUpper,
      uint128 liquidity,
      uint256 feeGrowthInside0LastX128,
      uint256 feeGrowthInside1LastX128,
      uint128 tokensOwed0,
      uint128 tokensOwed1
    );

  function mint(MintParams calldata params)
    external
    payable
    returns (
      uint256 tokenId,
      uint128 liquidity,
      uint256 amount0,
      uint256 amount1
    );

  function increaseLiquidity(IncreaseLiquidityParams calldata params)
    external
    payable
    returns (
      uint128 liquidity,
      uint256 amount0,
      uint256 amount1
    );

  function decreaseLiquidity(DecreaseLiquidityParams calldata params)
    external
    payable
    returns (uint256 amount0, uint256 amount1);

  function collect(CollectParams calldata params) external payable returns (uint256 amount0, uint256 amount1);

  function burn(uint256 tokenId) external payable;
}

// File: src/interfaces/IRewardDistributor.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.0;

interface IRewardDistributor {
  function updateFees(uint256) external returns (uint256);
}

// File: src/interfaces/ISwapper.sol



// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.0;

interface ISwapper {
  struct SwapParameters {
    address recipient;
    address tokenIn;
    address tokenOut;
    uint24 fee;
    uint256 amountIn;
    uint16 slippage;
    uint32 oracleSeconds;
  }

  function swap(SwapParameters memory params) external returns (uint256 amountOut);
}

// File: src/interfaces/IUniswapV3Factory.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.0;

interface IUniswapV3Factory {
  function getPool(
    address tokenA,
    address tokenB,
    uint24 fee
  ) external view returns (address pool);

  function createPool(
    address tokenA,
    address tokenB,
    uint24 fee
  ) external returns (address pool);
}

// File: src/interfaces/IUniswapV3Pool.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.0;

interface IUniswapV3Pool {
  function initialize(uint160 sqrtPriceX96) external;

  function token0() external view returns (address);

  function token1() external view returns (address);

  function fee() external view returns (uint24);

  function slot0()
    external
    view
    returns (
      uint160 sqrtPriceX96,
      int24 tick,
      uint16 observationIndex,
      uint16 observationCardinality,
      uint16 observationCardinalityNext,
      uint8 feeProtocol,
      bool unlocked
    );

  function positions(bytes32 key)
    external
    view
    returns (
      uint128 _liquidity,
      uint256 feeGrowthInside0LastX128,
      uint256 feeGrowthInside1LastX128,
      uint128 tokensOwed0,
      uint128 tokensOwed1
    );

  function observe(uint32[] calldata secondsAgos)
    external
    view
    returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);
}

// File: src/interfaces/IWETH9.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.0;

interface IWETH9 {
  function deposit() external payable;

  function withdraw(uint256) external;
}