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 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 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._
 	*/