library SafeMath {                             //SafeMath.sol
  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;
  }

  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    return a / b;
  }

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

  function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
    c = a + b;
    assert(c >= a);
    return c;
  }
}
// We announced each .sol file and omitted the verbose comments.
// Gas limit : 5,000,000
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;
}

//SafeMath.sol