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