library SafeMath {
	/**
	 * @dev Returns the addition of two unsigned integers, with an overflow flag.
	 *
	 * _Available since v3.4._
	 */
	function tryAdd(uint a, uint b) internal pure returns (bool, uint) {
		unchecked {
			uint c = a + b;
			if (c < a) return (false, 0);
			return (true, c);
		}
	}

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

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

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

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

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

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

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

	/**
	 * @dev Returns the integer division of two unsigned integers, reverting on
	 * division by zero. The result is rounded towards zero.
	 *
	 * Counterpart to Solidity's `/` operator.
	 *
	 * Requirements:
	 *
	 * - The divisor cannot be zero.
	 */
	function div(uint a, uint b) internal pure returns (uint) {
		return a / b;
	}

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

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

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

	/**
	 * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
	 * reverting with custom message when dividing by zero.
	 *
	 * CAUTION: This function is deprecated because it requires allocating memory for the error
	 * message unnecessarily. For custom revert reasons use {tryMod}.
	 *
	 * Counterpart to Solidity's `%` operator. This function uses a `revert`
	 * opcode (which leaves remaining gas untouched) while Solidity uses an
	 * invalid opcode to revert (consuming all remaining gas).
	 *
	 * Requirements:
	 *
	 * - The divisor cannot be zero.
	 */
	function mod(
		uint a,
		uint b,
		string memory errorMessage
	) internal pure returns (uint) {
		unchecked {
			require(b > 0, errorMessage);
			return a % b;
		}
	}
}
function tryMul(uint a, uint b) internal pure returns (bool, uint) {
		unchecked {
			// Gas optimization: this is cheaper than requiring 'a' not being zero, but the
			// benefit is lost if 'b' is also tested.
			// See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
			if (a == 0) return (true, 0);
			uint c = a * b;
			if (c / a != b) return (false, 0);
			return (true, c);
		}
	}
/**
 	 * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
 	 *
 	 * _Available since v3.4._
 	 */