library SafeMath {

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

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

    return c;
  }
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b > 0); 
    uint256 c = a / b;

    return c;
  }
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b <= a);
    uint256 c = a - b;

    return c;
  }
  
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    require(c >= a);

    return c;
  }
  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 mul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0) {
      return 0;
    }

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

    return c;
  }
/**
 * @dev Multiplies two numbers, reverts on overflow.
 */