library SafeMath {

   /**
    * @dev Multiplies two numbers, throws on overflow.
    */
   function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
       // Gas optimization: this is cheaper than asserting '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;
       }

       c = a * b;
       assert(c / a == b);
       return c;
   }

   /**
    * @dev Integer division of two numbers, truncating the quotient.
    */
   function div(uint256 a, uint256 b) internal pure returns (uint256) {
       // assert(b > 0); // Solidity automatically throws 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 a / b;
   }

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

   /**
    * @dev Adds two numbers, throws on overflow.
    */
   function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
       c = a + b;
       assert(c >= a);
       return c;
   }
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    assert(b <= a);
    return a - b;
}

/**
 * @dev Subtracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
 */