library SafeMath {
  /**
  * @dev Multiplies two numbers, reverts on 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-solidity/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b);

        return c;
    }

  /**
  * @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
  */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0); // Solidity only automatically asserts when dividing by 0
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

  /**
  * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
  */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a);
        uint256 c = a - b;

        return c;
    }

  /**
  * @dev Adds two numbers, reverts on overflow.
  */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a);

        return c;
    }

  /**
  * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
  * reverts when dividing by zero.
  */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0);
        return a % b;
    }
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that revert on error
 */
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a);
        uint256 c = a - b;

        return c;
    }
/**
 * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
 */