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

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

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

/**
* @dev Returns the subtraction of two unsigned integers, reverting with custom message on
* overflow (when the result is negative).
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {trySub}.
*
* Counterpart to Solidity's `-` operator.
*
* Requirements:
*
* - Subtraction cannot overflow.
*/
function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
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. This function uses a `revert`
* opcode (which leaves remaining gas untouched) while Solidity uses an
* invalid opcode to revert (consuming all remaining gas).
*
* Counterpart to Solidity's `/` operator. Note: this function uses a
* `revert` opcode (which leaves remaining gas untouched) while Solidity
* uses an invalid opcode to revert (consuming all remaining gas).
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
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(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
unchecked {
require(b > 0, errorMessage);
return a % b;
}
}
}
/**
 * @dev Wrappers over Solidity's arithmetic operations.
 *
 * NOTE: `SafeMath` is no longer needed starting with Solidity 0.8. The compiler
 * now has built in overflow checking.
 */
function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
unchecked {
require(b > 0, 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. This function uses a `revert`
 * opcode (which leaves remaining gas untouched) while Solidity uses an
 * invalid opcode to revert (consuming all remaining gas).
 *
 * 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.
 */