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