pragma solidity >=0.4.24;

/**
 * @dev Math operations with safety checks that throw on error. This contract is based
 * on the source code at https://goo.gl/iyQsmU.
 */
library SafeMath {
  /**
   * @dev Multiplies two numbers, throws on overflow.
   * @param _a Factor number.
   * @param _b Factor number.
   */
  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.
   * @param _a Dividend number.
   * @param _b Divisor number.
   */
  function div(uint256 _a, uint256 _b) internal pure returns (uint256) {
    uint256 c = _a / _b;
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }

  /**
   * @dev Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
   * @param _a Minuend number.
   * @param _b Subtrahend number.
   */
  function sub(uint256 _a, uint256 _b) internal pure returns (uint256) {
    assert(_b <= _a);
    return _a - _b;
  }

  /**
   * @dev Adds two numbers, throws on overflow.
   * @param _a Number.
   * @param _b Number.
   */
  function add(uint256 _a, uint256 _b) internal pure returns (uint256) {
    uint256 c = _a + _b;
    assert(c >= _a);
    return c;
  }

  function mod(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b != 0, "can not mod zero");
    return a % b;
  }
}