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) {
		uint256 c = a + b;
		require(c >= a, "SafeMath: addition overflow");

		return c;
	}

	/**
	 * @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 sub(a, b, "SafeMath: subtraction overflow");
	}

	/**
	 * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
	 * overflow (when the result is negative).
	 *
	 * Counterpart to Solidity's `-` operator.
	 *
	 * Requirements:
	 * - Subtraction cannot overflow.
	 *
	 * _Available since v2.4.0._
	 */
	function sub(uint256 a, uint256 b, string memory errorMessage)
		internal
		pure
		returns (uint256)
	{
		require(b <= a, errorMessage);
		uint256 c = a - b;

		return c;
	}

	/**
	 * @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) {
		// 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 0;
		}

		uint256 c = a * b;
		require(c / a == b, "SafeMath: multiplication overflow");

		return c;
	}

	/**
	 * @dev Returns the integer division of two unsigned integers. Reverts 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(uint256 a, uint256 b) internal pure returns (uint256) {
		return div(a, b, "SafeMath: division by zero");
	}

	/**
	 * @dev Returns the integer division of two unsigned integers. Reverts 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.
	 *
	 * _Available since v2.4.0._
	 */
	function div(uint256 a, uint256 b, string memory errorMessage)
		internal
		pure
		returns (uint256)
	{
		// Solidity only automatically asserts when dividing by 0
		require(b > 0, errorMessage);
		uint256 c = a / b;
		// assert(a == b * c + a % b); // There is no case in which this doesn't hold

		return c;
	}

	/**
	 * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
	 * Reverts 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 mod(a, b, "SafeMath: modulo by zero");
	}

	/**
	 * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
	 * Reverts with custom message 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.
	 *
	 * _Available since v2.4.0._
	 */
	function mod(uint256 a, uint256 b, string memory errorMessage)
		internal
		pure
		returns (uint256)
	{
		require(b != 0, errorMessage);
		return a % b;
	}
}
/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when 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.
 */
function mod(uint256 a, uint256 b, string memory errorMessage)
		internal
		pure
		returns (uint256)
	{
		require(b != 0, errorMessage);
		return a % b;
	}
/**
 	 * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
 	 * Reverts with custom message 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.
 	 *
 	 * _Available since v2.4.0._
 	 */