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



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

pragma solidity ^0.8.0;

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

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

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

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



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

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

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



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

pragma solidity ^0.8.0;

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

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

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



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

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 */
library Counters {
    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

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

    function increment(Counter storage counter) internal {
        unchecked {
            counter._value += 1;
        }
    }

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

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

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        require(value <= type(uint248).max, "SafeCast: value doesn't fit in 248 bits");
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        require(value <= type(uint240).max, "SafeCast: value doesn't fit in 240 bits");
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        require(value <= type(uint232).max, "SafeCast: value doesn't fit in 232 bits");
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.2._
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        require(value <= type(uint216).max, "SafeCast: value doesn't fit in 216 bits");
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        require(value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        require(value <= type(uint200).max, "SafeCast: value doesn't fit in 200 bits");
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        require(value <= type(uint192).max, "SafeCast: value doesn't fit in 192 bits");
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        require(value <= type(uint184).max, "SafeCast: value doesn't fit in 184 bits");
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        require(value <= type(uint176).max, "SafeCast: value doesn't fit in 176 bits");
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        require(value <= type(uint168).max, "SafeCast: value doesn't fit in 168 bits");
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        require(value <= type(uint160).max, "SafeCast: value doesn't fit in 160 bits");
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        require(value <= type(uint152).max, "SafeCast: value doesn't fit in 152 bits");
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        require(value <= type(uint144).max, "SafeCast: value doesn't fit in 144 bits");
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        require(value <= type(uint136).max, "SafeCast: value doesn't fit in 136 bits");
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v2.5._
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        require(value <= type(uint120).max, "SafeCast: value doesn't fit in 120 bits");
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        require(value <= type(uint112).max, "SafeCast: value doesn't fit in 112 bits");
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        require(value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.2._
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        require(value <= type(uint88).max, "SafeCast: value doesn't fit in 88 bits");
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        require(value <= type(uint80).max, "SafeCast: value doesn't fit in 80 bits");
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        require(value <= type(uint72).max, "SafeCast: value doesn't fit in 72 bits");
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v2.5._
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        require(value <= type(uint56).max, "SafeCast: value doesn't fit in 56 bits");
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        require(value <= type(uint48).max, "SafeCast: value doesn't fit in 48 bits");
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        require(value <= type(uint40).max, "SafeCast: value doesn't fit in 40 bits");
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v2.5._
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        require(value <= type(uint24).max, "SafeCast: value doesn't fit in 24 bits");
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v2.5._
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v2.5._
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     *
     * _Available since v3.0._
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 248 bits");
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 240 bits");
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 232 bits");
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.7._
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 224 bits");
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 216 bits");
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 208 bits");
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 200 bits");
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 192 bits");
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 184 bits");
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 176 bits");
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 168 bits");
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 160 bits");
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 152 bits");
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 144 bits");
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 136 bits");
    }

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

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 120 bits");
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 112 bits");
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 104 bits");
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.7._
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 96 bits");
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 88 bits");
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 80 bits");
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 72 bits");
    }

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

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 56 bits");
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 48 bits");
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 40 bits");
    }

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

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 24 bits");
    }

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

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

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     *
     * _Available since v3.0._
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// File: @openzeppelin/contracts/utils/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: contracts/core/interfaces/ISmardexFactory.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.8.17;

interface ISmardexFactory {
    /**
     * @notice emitted at each SmardexPair created
     * @param token0 address of the token0
     * @param token1 address of the token1
     * @param pair address of the SmardexPair created
     * @param totalPair number of SmardexPair created so far
     */
    event PairCreated(address indexed token0, address indexed token1, address pair, uint256 totalPair);

    /**
     * @notice return which address fees will be transferred
     */
    function feeTo() external view returns (address);

    /**
     * @notice return which address can update feeTo
     */
    function feeToSetter() external view returns (address);

    /**
     * @notice return the address of the pair of 2 tokens
     */
    function getPair(address _tokenA, address _tokenB) external view returns (address pair_);

    /**
     * @notice return the address of the pair at index
     * @param _index index of the pair
     * @return pair_ address of the pair
     */
    function allPairs(uint256 _index) external view returns (address pair_);

    /**
     * @notice return the quantity of pairs
     * @return quantity in uint256
     */
    function allPairsLength() external view returns (uint256);

    /**
     * @notice create pair with 2 address
     * @param _tokenA address of tokenA
     * @param _tokenB address of tokenB
     * @return pair_ address of the pair created
     */
    function createPair(address _tokenA, address _tokenB) external returns (address pair_);

    /**
     * @notice set the address who will receive fees, can only be call by feeToSetter
     * @param _feeTo address to replace
     */
    function setFeeTo(address _feeTo) external;

    /**
     * @notice set the address who can update feeTo, can only be call by feeToSetter
     * @param _feeToSetter address to replace
     */
    function setFeeToSetter(address _feeToSetter) external;
}

// File: contracts/core/interfaces/ISmardexMintCallback.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.8.17;

interface ISmardexMintCallback {
    /**
     * @notice callback data for mint
     * @param token0 address of the first token of the pair
     * @param token1 address of the second token of the pair
     * @param amount0 amount of token0 to provide
     * @param amount1 amount of token1 to provide
     * @param payer address of the payer to provide token for the mint
     */
    struct MintCallbackData {
        address token0;
        address token1;
        uint256 amount0;
        uint256 amount1;
        address payer;
    }

    /**
     * @notice callback to implement when calling SmardexPair.mint
     * @param _data callback data for mint
     */
    function smardexMintCallback(MintCallbackData calldata _data) external;
}

// File: contracts/core/interfaces/ISmardexPair.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.17;

// interfaces
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol";

interface ISmardexPair is IERC20, IERC20Permit {
    /**
     * @notice emitted at each mint
     * @param sender address calling the mint function (usualy the Router contract)
     * @param to address that receives the LP-tokens
     * @param amount0 amount of token0 to be added in liquidity
     * @param amount1 amount of token1 to be added in liquidity
     * @dev the amount of LP-token sent can be caught using the transfer event of the pair
     */
    event Mint(address indexed sender, address indexed to, uint256 amount0, uint256 amount1);

    /**
     * @notice emitted at each burn
     * @param sender address calling the burn function (usualy the Router contract)
     * @param to address that receives the tokens
     * @param amount0 amount of token0 to be withdrawn
     * @param amount1 amount of token1 to be withdrawn
     * @dev the amount of LP-token sent can be caught using the transfer event of the pair
     */
    event Burn(address indexed sender, address indexed to, uint256 amount0, uint256 amount1);

    /**
     * @notice emitted at each swap
     * @param sender address calling the swap function (usualy the Router contract)
     * @param to address that receives the out-tokens
     * @param amount0 amount of token0 to be swapped
     * @param amount1 amount of token1 to be swapped
     * @dev one of the 2 amount is always negative, the other one is always positive. The positive one is the one that
     * the user send to the contract, the negative one is the one that the contract send to the user.
     */
    event Swap(address indexed sender, address indexed to, int256 amount0, int256 amount1);

    /**
     * @notice emitted each time the fictive reserves are changed (mint, burn, swap)
     * @param reserve0 the new reserve of token0
     * @param reserve1 the new reserve of token1
     * @param fictiveReserve0 the new fictive reserve of token0
     * @param fictiveReserve1 the new fictive reserve of token1
     * @param priceAverage0 the new priceAverage of token0
     * @param priceAverage1 the new priceAverage of token1
     */
    event Sync(
        uint256 reserve0,
        uint256 reserve1,
        uint256 fictiveReserve0,
        uint256 fictiveReserve1,
        uint256 priceAverage0,
        uint256 priceAverage1
    );

    /**
     * @notice get the factory address
     * @return address of the factory
     */
    function factory() external view returns (address);

    /**
     * @notice get the token0 address
     * @return address of the token0
     */
    function token0() external view returns (address);

    /**
     * @notice get the token1 address
     * @return address of the token1
     */
    function token1() external view returns (address);

    /**
     * @notice called once by the factory at time of deployment
     * @param _token0 address of token0
     * @param _token1 address of token1
     */
    function initialize(address _token0, address _token1) external;

    /**
     * @notice return current Reserves of both token in the pair,
     *  corresponding to token balance - pending fees
     * @return reserve0_ current reserve of token0 - pending fee0
     * @return reserve1_ current reserve of token1 - pending fee1
     */
    function getReserves() external view returns (uint256 reserve0_, uint256 reserve1_);

    /**
     * @notice return current Fictives Reserves of both token in the pair
     * @return fictiveReserve0_ current fictive reserve of token0
     * @return fictiveReserve1_ current fictive reserve of token1
     */
    function getFictiveReserves() external view returns (uint256 fictiveReserve0_, uint256 fictiveReserve1_);

    /**
     * @notice return current pending fees of both token in the pair
     * @return fees0_ current pending fees of token0
     * @return fees1_ current pending fees of token1
     */
    function getFees() external view returns (uint256 fees0_, uint256 fees1_);

    /**
     * @notice return last updated price average at timestamp of both token in the pair,
     *  read price0Average/price1Average for current price of token0/token1
     * @return priceAverage0_ current price for token0
     * @return priceAverage1_ current price for token1
     * @return blockTimestampLast_ last block timestamp when price was updated
     */
    function getPriceAverage()
        external
        view
        returns (uint256 priceAverage0_, uint256 priceAverage1_, uint256 blockTimestampLast_);

    /**
     * @notice return current price average of both token in the pair for provided currentTimeStamp
     *  read price0Average/price1Average for current price of token0/token1
     * @param _fictiveReserveIn,
     * @param _fictiveReserveOut,
     * @param _priceAverageLastTimestamp,
     * @param _priceAverageIn current price for token0
     * @param _priceAverageOut current price for token1
     * @param _currentTimestamp block timestamp to get price
     * @return priceAverageIn_ current price for token0
     * @return priceAverageOut_ current price for token1
     */
    function getUpdatedPriceAverage(
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageLastTimestamp,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut,
        uint256 _currentTimestamp
    ) external pure returns (uint256 priceAverageIn_, uint256 priceAverageOut_);

    /**
     * @notice Mint lp tokens proportionally of added tokens in balance. Should be called from a contract
     * that makes safety checks like the SmardexRouter
     * @param _to address who will receive minted tokens
     * @param _amount0 amount of token0 to provide
     * @param _amount1 amount of token1 to provide
     * @return liquidity_ amount of lp tokens minted and sent to the address defined in parameter
     */
    function mint(
        address _to,
        uint256 _amount0,
        uint256 _amount1,
        address _payer
    ) external returns (uint256 liquidity_);

    /**
     * @notice Burn lp tokens in the balance of the contract. Sends to the defined address the amount of token0 and
     * token1 proportionally of the amount burned. Should be called from a contract that makes safety checks like the
     * SmardexRouter
     * @param _to address who will receive tokens
     * @return amount0_ amount of token0 sent to the address defined in parameter
     * @return amount1_ amount of token0 sent to the address defined in parameter
     */
    function burn(address _to) external returns (uint256 amount0_, uint256 amount1_);

    /**
     * @notice Swaps tokens. Sends to the defined address the amount of token0 and token1 defined in parameters.
     * Tokens to trade should be already sent in the contract.
     * Swap function will check if the resulted balance is correct with current reserves and reserves fictive.
     * Should be called from a contract that makes safety checks like the SmardexRouter
     * @param _to address who will receive tokens
     * @param _zeroForOne token0 to token1
     * @param _amountSpecified amount of token wanted
     * @param _data used for flash swap, data.length must be 0 for regular swap
     */
    function swap(
        address _to,
        bool _zeroForOne,
        int256 _amountSpecified,
        bytes calldata _data
    ) external returns (int256 amount0_, int256 amount1_);
}

// File: contracts/core/interfaces/ISmardexSwapCallback.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.8.17;

interface ISmardexSwapCallback {
    /**
     * @notice callback data for swap
     * @param _amount0Delta amount of token0 for the swap (negative is incoming, positive is required to pay to pair)
     * @param _amount1Delta amount of token1 for the swap (negative is incoming, positive is required to pay to pair)
     * @param _data for Router path and payer for the swap (see router for details)
     */
    function smardexSwapCallback(int256 _amount0Delta, int256 _amount1Delta, bytes calldata _data) external;
}

// File: contracts/core/libraries/SmardexLibrary.sol



// SPDX-License-Identifier: BUSL-1.1
pragma solidity =0.8.17;

// libraries
import "@openzeppelin/contracts/utils/math/Math.sol";

// interfaces
import "../interfaces/ISmardexPair.sol";

library SmardexLibrary {
    /// @notice amount of fees sent to LP, not in percent but in FEES_BASE
    uint256 public constant FEES_LP = 5;

    /// @notice amount of fees sent to the pool, not in percent but in FEES_BASE. if feeTo is null, sent to the LP
    uint256 public constant FEES_POOL = 2;

    /// @notice total amount of fees, not in percent but in FEES_BASE
    uint256 public constant FEES_TOTAL = FEES_LP + FEES_POOL;

    /// @notice base of the FEES
    uint256 public constant FEES_BASE = 10000;

    /// @notice ratio of quantity that is send to the user, after removing the fees, not in percent but in FEES_BASE
    uint256 public constant REVERSE_FEES_TOTAL = FEES_BASE - FEES_TOTAL;

    /// @notice precision for approxEq, not in percent but in APPROX_PRECISION_BASE
    uint256 public constant APPROX_PRECISION = 1;

    /// @notice base of the APPROX_PRECISION
    uint256 public constant APPROX_PRECISION_BASE = 1_000_000;

    /// @notice number of seconds to reset priceAverage
    uint256 private constant MAX_BLOCK_DIFF_SECONDS = 300;

    /**
     * @notice check if 2 numbers are approximatively equal, using APPROX_PRECISION
     * @param _x number to compare
     * @param _y number to compare
     * @return true if numbers are approximatively equal, false otherwise
     */
    function approxEq(uint256 _x, uint256 _y) internal pure returns (bool) {
        if (_x > _y) {
            return _x < (_y + (_y * APPROX_PRECISION) / APPROX_PRECISION_BASE);
        } else {
            return _y < (_x + (_x * APPROX_PRECISION) / APPROX_PRECISION_BASE);
        }
    }

    /**
     * @notice check if 2 ratio are approximatively equal: _xNum _/ xDen ~= _yNum / _yDen
     * @param _xNum numerator of the first ratio to compare
     * @param _xDen denominator of the first ratio to compare
     * @param _yNum numerator of the second ratio to compare
     * @param _yDen denominator of the second ratio to compare
     * @return true if ratio are approximatively equal, false otherwise
     */
    function ratioApproxEq(uint256 _xNum, uint256 _xDen, uint256 _yNum, uint256 _yDen) internal pure returns (bool) {
        return approxEq(_xNum * _yDen, _xDen * _yNum);
    }

    /**
     * @notice update priceAverage given old timestamp, new timestamp and prices
     * @param _fictiveReserveIn ratio component of the new price of the in-token
     * @param _fictiveReserveOut ratio component of the new price of the out-token
     * @param _priceAverageLastTimestamp timestamp of the last priceAvregae update (0, if never updated)
     * @param _priceAverageIn ratio component of the last priceAverage of the in-token
     * @param _priceAverageOut ratio component of the last priceAverage of the out-token
     * @param _currentTimestamp timestamp of the priceAverage to update
     * @return newPriceAverageIn_ ratio component of the updated priceAverage of the in-token
     * @return newPriceAverageOut_ ratio component of the updated priceAverage of the out-token
     */
    function getUpdatedPriceAverage(
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageLastTimestamp,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut,
        uint256 _currentTimestamp
    ) internal pure returns (uint256 newPriceAverageIn_, uint256 newPriceAverageOut_) {
        require(_currentTimestamp >= _priceAverageLastTimestamp, "SmardexPair: INVALID_TIMESTAMP");

        // very first time
        if (_priceAverageLastTimestamp == 0) {
            newPriceAverageIn_ = _fictiveReserveIn;
            newPriceAverageOut_ = _fictiveReserveOut;
        }
        // another tx has been done in the same block
        else if (_priceAverageLastTimestamp == _currentTimestamp) {
            newPriceAverageIn_ = _priceAverageIn;
            newPriceAverageOut_ = _priceAverageOut;
        }
        // need to compute new linear-average price
        else {
            // compute new price:
            uint256 _timeDiff = Math.min(_currentTimestamp - _priceAverageLastTimestamp, MAX_BLOCK_DIFF_SECONDS);

            newPriceAverageIn_ = _fictiveReserveIn;
            newPriceAverageOut_ =
                (((MAX_BLOCK_DIFF_SECONDS - _timeDiff) * _priceAverageOut * newPriceAverageIn_) /
                    _priceAverageIn +
                    _timeDiff *
                    _fictiveReserveOut) /
                MAX_BLOCK_DIFF_SECONDS;
        }
    }

    /**
     * @notice compute the firstTradeAmountIn so that the price reach the price Average
     * @param _amountIn the amountIn requested, it's the maximum possible value for firstAmountIn_
     * @param _fictiveReserveIn fictive reserve of the in-token
     * @param _fictiveReserveOut fictive reserve of the out-token
     * @param _priceAverageIn ratio component of the priceAverage of the in-token
     * @param _priceAverageOut ratio component of the priceAverage of the out-token
     * @return firstAmountIn_ the first amount of in-token
     *
     * @dev if the trade is going in the direction that the price will never reach the priceAverage, or if _amountIn
     * is not big enough to reach the priceAverage or if the price is already equal to the priceAverage, then
     * firstAmountIn_ will be set to _amountIn
     */
    function computeFirstTradeQtyIn(
        uint256 _amountIn,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut
    ) internal pure returns (uint256 firstAmountIn_) {
        // default value
        firstAmountIn_ = _amountIn;

        // if trade is in the good direction
        if (_fictiveReserveOut * _priceAverageIn > _fictiveReserveIn * _priceAverageOut) {
            // pre-compute all operands
            uint256 _toSub = _fictiveReserveIn * (FEES_BASE + REVERSE_FEES_TOTAL - FEES_POOL);
            uint256 _toDiv = (REVERSE_FEES_TOTAL + FEES_LP) << 1;
            uint256 _inSqrt = (((_fictiveReserveIn * _fictiveReserveOut) << 2) / _priceAverageOut) *
                _priceAverageIn *
                (REVERSE_FEES_TOTAL * (FEES_BASE - FEES_POOL)) +
                (_fictiveReserveIn * _fictiveReserveIn * (FEES_LP * FEES_LP));

            // reverse sqrt check to only compute sqrt if really needed
            if (_inSqrt < (_toSub + _amountIn * _toDiv) ** 2) {
                firstAmountIn_ = (Math.sqrt(_inSqrt) - _toSub) / _toDiv;
            }
        }
    }

    /**
     * @notice compute the firstTradeAmountOut so that the price reach the price Average
     * @param _amountOut the amountOut requested, it's the maximum possible value for firstAmountOut_
     * @param _fictiveReserveIn fictive reserve of the in-token
     * @param _fictiveReserveOut fictive reserve of the out-token
     * @param _priceAverageIn ratio component of the priceAverage of the in-token
     * @param _priceAverageOut ratio component of the priceAverage of the out-token
     * @return firstAmountOut_ the first amount of out-token
     *
     * @dev if the trade is going in the direction that the price will never reach the priceAverage, or if _amountOut
     * is not big enough to reach the priceAverage or if the price is already equal to the priceAverage, then
     * firstAmountOut_ will be set to _amountOut
     */
    function computeFirstTradeQtyOut(
        uint256 _amountOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut
    ) internal pure returns (uint256 firstAmountOut_) {
        // default value
        firstAmountOut_ = _amountOut;

        // if trade is in the good direction
        if (_fictiveReserveOut * _priceAverageIn > _fictiveReserveIn * _priceAverageOut) {
            // pre-compute all operands
            uint256 _fictiveReserveOutPredFees = (_fictiveReserveIn * FEES_LP * _priceAverageOut) / _priceAverageIn;
            uint256 _toAdd = ((_fictiveReserveOut * REVERSE_FEES_TOTAL) << 1) + _fictiveReserveOutPredFees;
            uint256 _toDiv = REVERSE_FEES_TOTAL << 1;
            uint256 _inSqrt = (((_fictiveReserveOut * _fictiveReserveOutPredFees) << 2) *
                (REVERSE_FEES_TOTAL * (FEES_BASE - FEES_POOL))) /
                FEES_LP +
                _fictiveReserveOutPredFees *
                _fictiveReserveOutPredFees;

            // reverse sqrt check to only compute sqrt if really needed
            if (_inSqrt > (_toAdd - _amountOut * _toDiv) ** 2) {
                firstAmountOut_ = (_toAdd - Math.sqrt(_inSqrt)) / _toDiv;
            }
        }
    }

    /**
     * @notice compute fictive reserves
     * @param _reserveIn reserve of the in-token
     * @param _reserveOut reserve of the out-token
     * @param _fictiveReserveIn fictive reserve of the in-token
     * @param _fictiveReserveOut fictive reserve of the out-token
     * @return newFictiveReserveIn_ new fictive reserve of the in-token
     * @return newFictiveReserveOut_ new fictive reserve of the out-token
     */
    function computeFictiveReserves(
        uint256 _reserveIn,
        uint256 _reserveOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut
    ) internal pure returns (uint256 newFictiveReserveIn_, uint256 newFictiveReserveOut_) {
        if (_reserveOut * _fictiveReserveIn < _reserveIn * _fictiveReserveOut) {
            uint256 _temp = (((_reserveOut * _reserveOut) / _fictiveReserveOut) * _fictiveReserveIn) / _reserveIn;
            newFictiveReserveIn_ =
                (_temp * _fictiveReserveIn) /
                _fictiveReserveOut +
                (_reserveOut * _fictiveReserveIn) /
                _fictiveReserveOut;
            newFictiveReserveOut_ = _reserveOut + _temp;
        } else {
            newFictiveReserveIn_ = (_fictiveReserveIn * _reserveOut) / _fictiveReserveOut + _reserveIn;
            newFictiveReserveOut_ = (_reserveIn * _fictiveReserveOut) / _fictiveReserveIn + _reserveOut;
        }

        // div all values by 4
        newFictiveReserveIn_ >>= 2;
        newFictiveReserveOut_ >>= 2;
    }

    /**
     * @notice apply k const rule using fictive reserve, when the amountIn is specified
     * @param _amountIn qty of token that arrives in the contract
     * @param _reserveIn reserve of the in-token
     * @param _reserveOut reserve of the out-token
     * @param _fictiveReserveIn fictive reserve of the in-token
     * @param _fictiveReserveOut fictive reserve of the out-token
     * @return amountOut_ qty of token that leaves in the contract
     * @return newReserveIn_ new reserve of the in-token after the transaction
     * @return newReserveOut_ new reserve of the out-token after the transaction
     * @return newFictiveReserveIn_ new fictive reserve of the in-token after the transaction
     * @return newFictiveReserveOut_ new fictive reserve of the out-token after the transaction
     */
    function applyKConstRuleOut(
        uint256 _amountIn,
        uint256 _reserveIn,
        uint256 _reserveOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut
    )
        internal
        pure
        returns (
            uint256 amountOut_,
            uint256 newReserveIn_,
            uint256 newReserveOut_,
            uint256 newFictiveReserveIn_,
            uint256 newFictiveReserveOut_
        )
    {
        // k const rule
        uint256 _amountInWithFee = _amountIn * REVERSE_FEES_TOTAL;
        uint256 _numerator = _amountInWithFee * _fictiveReserveOut;
        uint256 _denominator = _fictiveReserveIn * FEES_BASE + _amountInWithFee;
        amountOut_ = _numerator / _denominator;

        // update new reserves and add lp-fees to pools
        uint256 _amountInWithFeeLp = (_amountInWithFee + (_amountIn * FEES_LP)) / FEES_BASE;
        newReserveIn_ = _reserveIn + _amountInWithFeeLp;
        newFictiveReserveIn_ = _fictiveReserveIn + _amountInWithFeeLp;
        newReserveOut_ = _reserveOut - amountOut_;
        newFictiveReserveOut_ = _fictiveReserveOut - amountOut_;
    }

    /**
     * @notice apply k const rule using fictive reserve, when the amountOut is specified
     * @param _amountOut qty of token that leaves in the contract
     * @param _reserveIn reserve of the in-token
     * @param _reserveOut reserve of the out-token
     * @param _fictiveReserveIn fictive reserve of the in-token
     * @param _fictiveReserveOut fictive reserve of the out-token
     * @return amountIn_ qty of token that arrives in the contract
     * @return newReserveIn_ new reserve of the in-token after the transaction
     * @return newReserveOut_ new reserve of the out-token after the transaction
     * @return newFictiveReserveIn_ new fictive reserve of the in-token after the transaction
     * @return newFictiveReserveOut_ new fictive reserve of the out-token after the transaction
     */
    function applyKConstRuleIn(
        uint256 _amountOut,
        uint256 _reserveIn,
        uint256 _reserveOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut
    )
        internal
        pure
        returns (
            uint256 amountIn_,
            uint256 newReserveIn_,
            uint256 newReserveOut_,
            uint256 newFictiveReserveIn_,
            uint256 newFictiveReserveOut_
        )
    {
        // k const rule
        uint256 _numerator = _fictiveReserveIn * _amountOut * FEES_BASE;
        uint256 _denominator = (_fictiveReserveOut - _amountOut) * REVERSE_FEES_TOTAL;
        amountIn_ = _numerator / _denominator + 1;

        // update new reserves
        uint256 _amountInWithFeeLp = (amountIn_ * (REVERSE_FEES_TOTAL + FEES_LP)) / FEES_BASE;
        newReserveIn_ = _reserveIn + _amountInWithFeeLp;
        newFictiveReserveIn_ = _fictiveReserveIn + _amountInWithFeeLp;
        newReserveOut_ = _reserveOut - _amountOut;
        newFictiveReserveOut_ = _fictiveReserveOut - _amountOut;
    }

    /**
     * @notice return the amount of tokens the user would get by doing a swap
     * @param _amountIn quantity of token the user want to swap (to sell)
     * @param _reserveIn reserves of the selling token (getReserve())
     * @param _reserveOut reserves of the buying token (getReserve())
     * @param _fictiveReserveIn fictive reserve of the selling token (getFictiveReserves())
     * @param _fictiveReserveOut fictive reserve of the buying token (getFictiveReserves())
     * @param _priceAverageIn price average of the selling token
     * @param _priceAverageOut price average of the buying token
     * @return amountOut_ The amount of token the user would receive
     * @return newReserveIn_ reserves of the selling token after the swap
     * @return newReserveOut_ reserves of the buying token after the swap
     * @return newFictiveReserveIn_ fictive reserve of the selling token after the swap
     * @return newFictiveReserveOut_ fictive reserve of the buying token after the swap
     */
    function getAmountOut(
        uint256 _amountIn,
        uint256 _reserveIn,
        uint256 _reserveOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut
    )
        internal
        pure
        returns (
            uint256 amountOut_,
            uint256 newReserveIn_,
            uint256 newReserveOut_,
            uint256 newFictiveReserveIn_,
            uint256 newFictiveReserveOut_
        )
    {
        require(_amountIn > 0, "SmarDexLibrary: INSUFFICIENT_INPUT_AMOUNT");
        require(
            _reserveIn > 0 && _reserveOut > 0 && _fictiveReserveIn > 0 && _fictiveReserveOut > 0,
            "SmarDexLibrary: INSUFFICIENT_LIQUIDITY"
        );

        uint256 _amountInWithFees = (_amountIn * REVERSE_FEES_TOTAL) / FEES_BASE;
        uint256 _firstAmountIn = computeFirstTradeQtyIn(
            _amountInWithFees,
            _fictiveReserveIn,
            _fictiveReserveOut,
            _priceAverageIn,
            _priceAverageOut
        );

        // if there is 2 trade: 1st trade mustn't re-compute fictive reserves, 2nd should
        if (
            _firstAmountIn == _amountInWithFees &&
            ratioApproxEq(_fictiveReserveIn, _fictiveReserveOut, _priceAverageIn, _priceAverageOut)
        ) {
            (_fictiveReserveIn, _fictiveReserveOut) = computeFictiveReserves(
                _reserveIn,
                _reserveOut,
                _fictiveReserveIn,
                _fictiveReserveOut
            );
        }

        // avoid stack too deep
        {
            uint256 _firstAmountInNoFees = (_firstAmountIn * FEES_BASE) / REVERSE_FEES_TOTAL;
            (
                amountOut_,
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            ) = applyKConstRuleOut(
                _firstAmountInNoFees,
                _reserveIn,
                _reserveOut,
                _fictiveReserveIn,
                _fictiveReserveOut
            );

            // update amountIn in case there is a second trade
            _amountIn -= _firstAmountInNoFees;
        }

        // if we need a second trade
        if (_firstAmountIn < _amountInWithFees) {
            // in the second trade ALWAYS recompute fictive reserves
            (newFictiveReserveIn_, newFictiveReserveOut_) = computeFictiveReserves(
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            );

            uint256 _secondAmountOutNoFees;
            (
                _secondAmountOutNoFees,
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            ) = applyKConstRuleOut(
                _amountIn,
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            );
            amountOut_ += _secondAmountOutNoFees;
        }
    }

    /**
     * @notice return the amount of tokens the user should spend by doing a swap
     * @param _amountOut quantity of token the user want to swap (to buy)
     * @param _reserveIn reserves of the selling token (getReserve())
     * @param _reserveOut reserves of the buying token (getReserve())
     * @param _fictiveReserveIn fictive reserve of the selling token (getFictiveReserves())
     * @param _fictiveReserveOut fictive reserve of the buying token (getFictiveReserves())
     * @param _priceAverageIn price average of the selling token
     * @param _priceAverageOut price average of the buying token
     * @return amountIn_ The amount of token the user would spend to receive _amountOut
     * @return newReserveIn_ reserves of the selling token after the swap
     * @return newReserveOut_ reserves of the buying token after the swap
     * @return newFictiveReserveIn_ fictive reserve of the selling token after the swap
     * @return newFictiveReserveOut_ fictive reserve of the buying token after the swap
     */
    function getAmountIn(
        uint256 _amountOut,
        uint256 _reserveIn,
        uint256 _reserveOut,
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut
    )
        internal
        pure
        returns (
            uint256 amountIn_,
            uint256 newReserveIn_,
            uint256 newReserveOut_,
            uint256 newFictiveReserveIn_,
            uint256 newFictiveReserveOut_
        )
    {
        require(_amountOut > 0, "SmarDexLibrary: INSUFFICIENT_OUTPUT_AMOUNT");
        require(
            _amountOut < _fictiveReserveOut &&
                _reserveIn > 0 &&
                _reserveOut > 0 &&
                _fictiveReserveIn > 0 &&
                _fictiveReserveOut > 0,
            "SmarDexLibrary: INSUFFICIENT_LIQUIDITY"
        );

        uint256 _firstAmountOut = computeFirstTradeQtyOut(
            _amountOut,
            _fictiveReserveIn,
            _fictiveReserveOut,
            _priceAverageIn,
            _priceAverageOut
        );

        // if there is 2 trade: 1st trade mustn't re-compute fictive reserves, 2nd should
        if (
            _firstAmountOut == _amountOut &&
            ratioApproxEq(_fictiveReserveIn, _fictiveReserveOut, _priceAverageIn, _priceAverageOut)
        ) {
            (_fictiveReserveIn, _fictiveReserveOut) = computeFictiveReserves(
                _reserveIn,
                _reserveOut,
                _fictiveReserveIn,
                _fictiveReserveOut
            );
        }

        (amountIn_, newReserveIn_, newReserveOut_, newFictiveReserveIn_, newFictiveReserveOut_) = applyKConstRuleIn(
            _firstAmountOut,
            _reserveIn,
            _reserveOut,
            _fictiveReserveIn,
            _fictiveReserveOut
        );

        // if we need a second trade
        if (_firstAmountOut < _amountOut) {
            // in the second trade ALWAYS recompute fictive reserves
            (newFictiveReserveIn_, newFictiveReserveOut_) = computeFictiveReserves(
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            );

            uint256 _secondAmountIn;
            (
                _secondAmountIn,
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            ) = applyKConstRuleIn(
                _amountOut - _firstAmountOut,
                newReserveIn_,
                newReserveOut_,
                newFictiveReserveIn_,
                newFictiveReserveOut_
            );
            amountIn_ += _secondAmountIn;
        }
    }
}

// File: contracts/core/libraries/TransferHelper.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity =0.8.17;

/**
 * @title TransferHelper
 * @notice helper methods for interacting with ERC20 tokens and sending ETH that do not consistently return true/false
 * @custom:from Uniswap lib, adapted to version 0.8.17
 * @custom:url https://github.com/Uniswap/solidity-lib/blob/master/contracts/libraries/TransferHelper.sol
 */
library TransferHelper {
    function safeApprove(address token, address to, uint256 value) internal {
        // bytes4(keccak256(bytes('approve(address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0x095ea7b3, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            "TransferHelper::safeApprove: approve failed"
        );
    }

    function safeTransfer(address token, address to, uint256 value) internal {
        // bytes4(keccak256(bytes('transfer(address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0xa9059cbb, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            "TransferHelper::safeTransfer: transfer failed"
        );
    }

    function safeTransferFrom(address token, address from, address to, uint256 value) internal {
        // bytes4(keccak256(bytes('transferFrom(address,address,uint256)')));
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(0x23b872dd, from, to, value));
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            "TransferHelper::transferFrom: transferFrom failed"
        );
    }

    function safeTransferETH(address to, uint256 value) internal {
        (bool success, ) = to.call{ value: value }(new bytes(0));
        require(success, "TransferHelper::safeTransferETH: ETH transfer failed");
    }
}

// File: contracts/core/SmardexPair.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity =0.8.17;

// contracts
import "@openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol";

// libraries
import "@openzeppelin/contracts/utils/math/SafeCast.sol";
import "./libraries/SmardexLibrary.sol";
import "./libraries/TransferHelper.sol";

// interfaces
import "./interfaces/ISmardexPair.sol";
import "./interfaces/ISmardexFactory.sol";
import "./interfaces/ISmardexSwapCallback.sol";
import "./interfaces/ISmardexMintCallback.sol";

/**
 * @title SmardexPair
 * @notice Pair contract that allows user to swap 2 ERC20-strict tokens in a decentralised and automated way
 */
contract SmardexPair is ISmardexPair, ERC20Permit {
    using SafeCast for uint256;
    using SafeCast for int256;

    /**
     * @notice swap parameters used by function swap
     * @param amountCalculated return amount from getAmountIn/Out is always positive but to avoid too much cast, is int
     * @param fictiveReserveIn fictive reserve of the in-token of the pair
     * @param fictiveReserveOut fictive reserve of the out-token of the pair
     * @param priceAverageIn in-token ratio component of the price average
     * @param priceAverageOut out-token ratio component of the price average
     * @param token0 address of the token0
     * @param token1 address of the token1
     * @param balanceIn contract balance of the in-token
     * @param balanceOut contract balance of the out-token
     */
    struct SwapParams {
        int256 amountCalculated;
        uint256 fictiveReserveIn;
        uint256 fictiveReserveOut;
        uint256 priceAverageIn;
        uint256 priceAverageOut;
        address token0;
        address token1;
        uint256 balanceIn;
        uint256 balanceOut;
    }

    uint8 private constant CONTRACT_UNLOCKED = 1;
    uint8 private constant CONTRACT_LOCKED = 2;
    uint256 private constant MINIMUM_LIQUIDITY = 10 ** 3;
    bytes4 private constant AUTOSWAP_SELECTOR = bytes4(keccak256(bytes("executeWork(address,address)")));

    address public factory;
    address public token0;
    address public token1;

    // smardex new fictive reserves
    uint128 internal fictiveReserve0;
    uint128 internal fictiveReserve1; // accessible via getFictiveReserves()

    // moving average on the price
    uint128 internal priceAverage0;
    uint128 internal priceAverage1;
    uint40 internal priceAverageLastTimestamp; // accessible via getPriceAverage()

    // fee for FEE_POOL
    uint104 internal feeToAmount0;
    uint104 internal feeToAmount1; // accessible via getFees()

    // reentrancy
    uint8 private lockStatus = CONTRACT_UNLOCKED;

    modifier lock() {
        require(lockStatus == CONTRACT_UNLOCKED, "SmarDex: LOCKED");
        lockStatus = CONTRACT_LOCKED;
        _;
        lockStatus = CONTRACT_UNLOCKED;
    }

    constructor() ERC20("SmarDex LP-Token", "SDEX-LP") ERC20Permit("SmarDex LP-Token") {
        factory = msg.sender;
    }

    ///@inheritdoc ISmardexPair
    function initialize(address _token0, address _token1) external override {
        require(msg.sender == factory, "SmarDex: FORBIDDEN"); // sufficient check
        token0 = _token0;
        token1 = _token1;
    }

    ///@inheritdoc ISmardexPair
    function getReserves() external view override returns (uint256 reserve0_, uint256 reserve1_) {
        reserve0_ = IERC20(token0).balanceOf(address(this)) - feeToAmount0;
        reserve1_ = IERC20(token1).balanceOf(address(this)) - feeToAmount1;
    }

    ///@inheritdoc ISmardexPair
    function getFictiveReserves() external view override returns (uint256 fictiveReserve0_, uint256 fictiveReserve1_) {
        fictiveReserve0_ = fictiveReserve0;
        fictiveReserve1_ = fictiveReserve1;
    }

    ///@inheritdoc ISmardexPair
    function getFees() external view override returns (uint256 fees0_, uint256 fees1_) {
        fees0_ = feeToAmount0;
        fees1_ = feeToAmount1;
    }

    ///@inheritdoc ISmardexPair
    function getPriceAverage()
        external
        view
        returns (uint256 priceAverage0_, uint256 priceAverage1_, uint256 priceAverageLastTimestamp_)
    {
        priceAverage0_ = priceAverage0;
        priceAverage1_ = priceAverage1;
        priceAverageLastTimestamp_ = priceAverageLastTimestamp;
    }

    ///@inheritdoc ISmardexPair
    function getUpdatedPriceAverage(
        uint256 _fictiveReserveIn,
        uint256 _fictiveReserveOut,
        uint256 _priceAverageLastTimestamp,
        uint256 _priceAverageIn,
        uint256 _priceAverageOut,
        uint256 _currentTimestamp
    ) public pure returns (uint256 priceAverageIn_, uint256 priceAverageOut_) {
        (priceAverageIn_, priceAverageOut_) = SmardexLibrary.getUpdatedPriceAverage(
            _fictiveReserveIn,
            _fictiveReserveOut,
            _priceAverageLastTimestamp,
            _priceAverageIn,
            _priceAverageOut,
            _currentTimestamp
        );
    }

    ///@inheritdoc ISmardexPair
    function mint(
        address _to,
        uint256 _amount0,
        uint256 _amount1,
        address _payer
    ) external override returns (uint256 liquidity_) {
        liquidity_ = _mintBeforeFee(_to, _amount0, _amount1, _payer);

        // we call feeTo out of the internal locked mint (_mintExt) function to be able to swap fees in here
        _feeToSwap();
    }

    ///@inheritdoc ISmardexPair
    function burn(address _to) external override returns (uint256 amount0_, uint256 amount1_) {
        (amount0_, amount1_) = _burnBeforeFee(_to);

        // we call feeTo out of the internal locked burn (_burnExt) function to be able to swap fees in here
        _feeToSwap();
    }

    ///@inheritdoc ISmardexPair
    function swap(
        address _to,
        bool _zeroForOne,
        int256 _amountSpecified,
        bytes calldata _data
    ) external override lock returns (int256 amount0_, int256 amount1_) {
        require(_amountSpecified != 0, "SmarDex: ZERO_AMOUNT");

        SwapParams memory _params = SwapParams({
            amountCalculated: 0,
            fictiveReserveIn: 0,
            fictiveReserveOut: 0,
            priceAverageIn: 0,
            priceAverageOut: 0,
            token0: token0,
            token1: token1,
            balanceIn: 0,
            balanceOut: 0
        });

        (
            _params.balanceIn,
            _params.balanceOut,
            _params.fictiveReserveIn,
            _params.fictiveReserveOut,
            _params.priceAverageIn,
            _params.priceAverageOut
        ) = _zeroForOne
            ? (
                IERC20(_params.token0).balanceOf(address(this)) - feeToAmount0,
                IERC20(_params.token1).balanceOf(address(this)) - feeToAmount1,
                fictiveReserve0,
                fictiveReserve1,
                priceAverage0,
                priceAverage1
            )
            : (
                IERC20(_params.token1).balanceOf(address(this)) - feeToAmount1,
                IERC20(_params.token0).balanceOf(address(this)) - feeToAmount0,
                fictiveReserve1,
                fictiveReserve0,
                priceAverage1,
                priceAverage0
            );

        // compute new price average
        (_params.priceAverageIn, _params.priceAverageOut) = SmardexLibrary.getUpdatedPriceAverage(
            _params.fictiveReserveIn,
            _params.fictiveReserveOut,
            priceAverageLastTimestamp,
            _params.priceAverageIn,
            _params.priceAverageOut,
            block.timestamp
        );

        // SSTORE new price average
        (priceAverage0, priceAverage1, priceAverageLastTimestamp) = _zeroForOne
            ? (_params.priceAverageIn.toUint128(), _params.priceAverageOut.toUint128(), uint40(block.timestamp))
            : (_params.priceAverageOut.toUint128(), _params.priceAverageIn.toUint128(), uint40(block.timestamp));

        if (_amountSpecified > 0) {
            uint256 _temp;
            (_temp, , , _params.fictiveReserveIn, _params.fictiveReserveOut) = SmardexLibrary.getAmountOut(
                _amountSpecified.toUint256(),
                _params.balanceIn,
                _params.balanceOut,
                _params.fictiveReserveIn,
                _params.fictiveReserveOut,
                _params.priceAverageIn,
                _params.priceAverageOut
            );
            _params.amountCalculated = _temp.toInt256();
        } else {
            uint256 _temp;
            (_temp, , , _params.fictiveReserveIn, _params.fictiveReserveOut) = SmardexLibrary.getAmountIn(
                (-_amountSpecified).toUint256(),
                _params.balanceIn,
                _params.balanceOut,
                _params.fictiveReserveIn,
                _params.fictiveReserveOut,
                _params.priceAverageIn,
                _params.priceAverageOut
            );
            _params.amountCalculated = _temp.toInt256();
        }

        (amount0_, amount1_) = _zeroForOne
            ? (
                _amountSpecified > 0
                    ? (_amountSpecified, -_params.amountCalculated)
                    : (_params.amountCalculated, _amountSpecified)
            )
            : (
                _amountSpecified > 0
                    ? (-_params.amountCalculated, _amountSpecified)
                    : (_amountSpecified, _params.amountCalculated)
            );

        require(_to != _params.token0 && _to != _params.token1, "SmarDex: INVALID_TO");
        if (_zeroForOne) {
            if (amount1_ < 0) {
                TransferHelper.safeTransfer(_params.token1, _to, uint256(-amount1_));
            }
            ISmardexSwapCallback(msg.sender).smardexSwapCallback(amount0_, amount1_, _data);
            uint256 _balanceInBefore = _params.balanceIn;
            _params.balanceIn = IERC20(token0).balanceOf(address(this));
            require(
                _balanceInBefore + feeToAmount0 + (amount0_).toUint256() <= _params.balanceIn,
                "SmarDex: INSUFFICIENT_TOKEN0_INPUT_AMOUNT"
            );
            _params.balanceOut = IERC20(token1).balanceOf(address(this));
        } else {
            if (amount0_ < 0) {
                TransferHelper.safeTransfer(_params.token0, _to, uint256(-amount0_));
            }
            ISmardexSwapCallback(msg.sender).smardexSwapCallback(amount0_, amount1_, _data);
            uint256 _balanceInBefore = _params.balanceIn;
            _params.balanceIn = IERC20(token1).balanceOf(address(this));
            require(
                _balanceInBefore + feeToAmount1 + (amount1_).toUint256() <= _params.balanceIn,
                "SmarDex: INSUFFICIENT_TOKEN1_INPUT_AMOUNT"
            );
            _params.balanceOut = IERC20(token0).balanceOf(address(this));
        }

        // update feeTopart
        bool _feeOn = ISmardexFactory(factory).feeTo() != address(0);
        if (_zeroForOne) {
            if (_feeOn) {
                feeToAmount0 += ((uint256(amount0_) * SmardexLibrary.FEES_POOL) / SmardexLibrary.FEES_BASE).toUint104();
            }
            _update(
                _params.balanceIn,
                _params.balanceOut,
                _params.fictiveReserveIn,
                _params.fictiveReserveOut,
                _params.priceAverageIn,
                _params.priceAverageOut
            );
        } else {
            if (_feeOn) {
                feeToAmount1 += ((uint256(amount1_) * SmardexLibrary.FEES_POOL) / SmardexLibrary.FEES_BASE).toUint104();
            }
            _update(
                _params.balanceOut,
                _params.balanceIn,
                _params.fictiveReserveOut,
                _params.fictiveReserveIn,
                _params.priceAverageOut,
                _params.priceAverageIn
            );
        }

        emit Swap(msg.sender, _to, amount0_, amount1_);
    }

    /**
     * @notice update fictive reserves and emit the Sync event
     * @param _balance0 the new balance of token0
     * @param _balance1 the new balance of token1
     * @param _fictiveReserve0 the new fictive reserves of token0
     * @param _fictiveReserve1 the new fictive reserves of token1
     * @param _priceAverage0 the new priceAverage of token0
     * @param _priceAverage1 the new priceAverage of token1
     */
    function _update(
        uint256 _balance0,
        uint256 _balance1,
        uint256 _fictiveReserve0,
        uint256 _fictiveReserve1,
        uint256 _priceAverage0,
        uint256 _priceAverage1
    ) private {
        require(_fictiveReserve0 > 0 && _fictiveReserve1 > 0, "SmarDex: FICTIVE_RESERVES_TOO_LOW");
        require(_fictiveReserve0 <= type(uint128).max && _fictiveReserve1 <= type(uint128).max, "SmarDex: OVERFLOW");
        fictiveReserve0 = uint128(_fictiveReserve0);
        fictiveReserve1 = uint128(_fictiveReserve1);

        emit Sync(
            _balance0 - feeToAmount0,
            _balance1 - feeToAmount1,
            _fictiveReserve0,
            _fictiveReserve1,
            _priceAverage0,
            _priceAverage1
        );
    }

    /**
     * @notice transfers feeToAmount of tokens 0 and 1 to feeTo, and reset feeToAmounts
     * @return feeOn_ if part of the fees goes to feeTo
     */
    function _mintFee() private returns (bool feeOn_) {
        address _feeTo = ISmardexFactory(factory).feeTo();
        feeOn_ = _feeTo != address(0);
        if (feeOn_) {
            // gas saving
            uint256 _feeToAmount0 = feeToAmount0;
            uint256 _feeToAmount1 = feeToAmount1;

            if (_feeToAmount0 > 0) {
                TransferHelper.safeTransfer(token0, _feeTo, _feeToAmount0);
                feeToAmount0 = 0;
            }
            if (_feeToAmount1 > 0) {
                TransferHelper.safeTransfer(token1, _feeTo, _feeToAmount1);
                feeToAmount1 = 0;
            }
        } else {
            feeToAmount0 = 0;
            feeToAmount1 = 0;
        }
    }

    /**
     * @notice Mint lp tokens proportionally of added tokens in balance.
     * @param _to address who will receive minted tokens
     * @param _amount0 amount of token0 to provide
     * @param _amount1 amount of token1 to provide
     * @param _payer address of the payer to provide token for the mint
     * @return liquidity_ amount of lp tokens minted and sent to the address defined in parameter
     */
    function _mintBeforeFee(
        address _to,
        uint256 _amount0,
        uint256 _amount1,
        address _payer
    ) internal lock returns (uint256 liquidity_) {
        _mintFee();

        uint256 _fictiveReserve0;
        uint256 _fictiveReserve1;

        // gas saving
        uint256 _balance0 = IERC20(token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(token1).balanceOf(address(this));
        uint256 _totalSupply = totalSupply();

        ISmardexMintCallback(msg.sender).smardexMintCallback(
            ISmardexMintCallback.MintCallbackData({
                token0: token0,
                token1: token1,
                amount0: _amount0,
                amount1: _amount1,
                payer: _payer
            })
        );

        // gas savings
        uint256 _balance0after = IERC20(token0).balanceOf(address(this));
        uint256 _balance1after = IERC20(token1).balanceOf(address(this));

        require(_balance0after >= _balance0 + _amount0, "SmarDex: INSUFFICIENT_AMOUNT_0");
        require(_balance1after >= _balance1 + _amount1, "SmarDex: INSUFFICIENT_AMOUNT_1");

        if (_totalSupply == 0) {
            liquidity_ = Math.sqrt(_amount0 * _amount1) - MINIMUM_LIQUIDITY;
            _mint(address(0xdead), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens
            _fictiveReserve0 = _balance0after / 2;
            _fictiveReserve1 = _balance1after / 2;
        } else {
            liquidity_ = Math.min((_amount0 * _totalSupply) / _balance0, (_amount1 * _totalSupply) / _balance1);

            // update proportionally the fictiveReserves
            _fictiveReserve0 = (fictiveReserve0 * (_totalSupply + liquidity_)) / _totalSupply;
            _fictiveReserve1 = (fictiveReserve1 * (_totalSupply + liquidity_)) / _totalSupply;
        }

        require(liquidity_ > 0, "SmarDex: INSUFFICIENT_LIQUIDITY_MINTED");
        _mint(_to, liquidity_);

        _update(_balance0after, _balance1after, _fictiveReserve0, _fictiveReserve1, priceAverage0, priceAverage1);

        emit Mint(msg.sender, _to, _amount0, _amount1);
    }

    /**
     * @notice Burn lp tokens in the balance of the contract. Sends to the defined address the amount of token0 and
     * token1 proportionally of the amount burned.
     * @param _to address who will receive tokens
     * @return amount0_ amount of token0 sent to the address defined in parameter
     * @return amount1_ amount of token0 sent to the address defined in parameter
     */
    function _burnBeforeFee(address _to) internal lock returns (uint256 amount0_, uint256 amount1_) {
        _mintFee();

        // gas savings
        address _token0 = token0;
        address _token1 = token1;
        uint256 _balance0 = IERC20(_token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(_token1).balanceOf(address(this));
        uint256 _liquidity = balanceOf(address(this));
        uint256 _totalSupply = totalSupply();

        // pro-rata distribution
        amount0_ = (_liquidity * _balance0) / _totalSupply;
        amount1_ = (_liquidity * _balance1) / _totalSupply;
        require(amount0_ > 0 && amount1_ > 0, "SmarDex: INSUFFICIENT_LIQUIDITY_BURNED");

        // update proportionally the fictiveReserves
        uint256 _fictiveReserve0 = fictiveReserve0;
        uint256 _fictiveReserve1 = fictiveReserve1;
        _fictiveReserve0 -= (_fictiveReserve0 * _liquidity) / _totalSupply;
        _fictiveReserve1 -= (_fictiveReserve1 * _liquidity) / _totalSupply;

        _burn(address(this), _liquidity);
        TransferHelper.safeTransfer(_token0, _to, amount0_);
        TransferHelper.safeTransfer(_token1, _to, amount1_);

        _balance0 = IERC20(_token0).balanceOf(address(this));
        _balance1 = IERC20(_token1).balanceOf(address(this));

        _update(_balance0, _balance1, _fictiveReserve0, _fictiveReserve1, priceAverage0, priceAverage1);

        emit Burn(msg.sender, _to, amount0_, amount1_);
    }

    /**
     * @notice execute function "executeWork(address,address)" of the feeTo contract. Doesn't revert tx if it reverts
     */
    function _feeToSwap() internal {
        address _feeTo = ISmardexFactory(factory).feeTo();

        // call contract destination for handling fees
        // We don't handle return values so it does not revert for LP if something went wrong in feeTo
        _feeTo.call(abi.encodeWithSelector(AUTOSWAP_SELECTOR, token0, token1));
    }
}