library SafeMath {

  /**
  * @dev Multiplies two unsigned integers, throws on overflow.
  */
  function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
    // Gas optimization: this is cheaper than asserting '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;
    }

    c = a * b;
    assert(c / a == b);
    return c;
  }

  /**
  * @dev Multiplies two signed integers, throws on overflow.
  */
  function mul(int256 a, int256 b) internal pure returns (int256) {
    // Gas optimization: this is cheaper than asserting '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;
    }
    int256 c = a * b;
    assert(c / a == b);
    return c;
  }

  /**
  * @dev Integer division of two unsigned integers, 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 a / b;
  }

  /**
  * @dev Integer division of two signed integers, truncating the quotient.
  */
  function div(int256 a, int256 b) internal pure returns (int256) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    // Overflow only happens when the smallest negative int is multiplied by -1.
    int256 INT256_MIN = int256((uint256(1) << 255));
    assert(a != INT256_MIN || b != -1);
    return a / b;
  }

  /**
  * @dev Subtracts two unsigned integers, 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 Subtracts two signed integers, throws on overflow.
  */
  function sub(int256 a, int256 b) internal pure returns (int256) {
    int256 c = a - b;
    assert((b >= 0 && c <= a) || (b < 0 && c > a));
    return c;
  }

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

  /**
  * @dev Adds two signed integers, throws on overflow.
  */
  function add(int256 a, int256 b) internal pure returns (int256) {
    int256 c = a + b;
    assert((b >= 0 && c >= a) || (b < 0 && c < a));
    return c;
  }
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 * Source: https://github.com/facuspagnuolo/zeppelin-solidity/blob/feature/705_add_safe_math_int_ops/contracts/math/SafeMath.sol
 */
function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
  // Gas optimization: this is cheaper than asserting '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;
  }

  c = a * b;
  assert(c / a == b);
  return c;
}

/**
 * @dev Multiplies two unsigned integers, throws on overflow.
 */