library SafeMath {
  /**
   * @dev Multiplies two unsigned integers, reverts on overflow.
   */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
    // benefit is lost if 'b' is also tested.
    // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
    if (a == 0) {
      return 0;
    }

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

    return c;
  }

  /**
   * @dev Integer division of two unsigned integers truncating the quotient, reverts on division by zero.
   */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    // Solidity only automatically asserts when dividing by 0
    require(b > 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 unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
   */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b <= a);
    uint256 c = a - b;

    return c;
  }

  /**
   * @dev Adds two unsigned integers, reverts on overflow.
   */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    require(c >= a);

    return c;
  }

  /**
   * @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo),
   * reverts when dividing by zero.
   */
  function mod(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b != 0);
    return a % b;
  }
}
/**
 * @title SafeMath
 * @dev Unsigned math operations with safety checks that revert on error.
 */
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b <= a);
    uint256 c = a - b;

    return c;
  }
/**
 * @dev Subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
 */