library SafeMath {
    
    /**
    * @dev Multiplies two numbers, throws on overflow.
    */
    function mul(uint256 a, uint256 b) 
        internal 
        pure 
        returns (uint256 c) 
    {
        if (a == 0) {
            return 0;
        }
        c = a * b;
        require(c / a == b);
        return c;
    }

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