The game of Nim (2) P49499

This is another problem about the game of Nim, which is thoroughly explained in problem ‍. But here, we may have a huge number of sets, each with a huge number of marbles.

Input

Input consists of several cases. Every case begins with the number of sets n, followed by the number of marbles of each set, all between 0 and 10⁹. Assume 0 ≤ n ≤ 10⁵.

Output

For every case, tell if it is a winning or a losing configuration.

Hint

You should use a mathematical trick to solve this problem.