The game of Nim (2)

This is another problem about the game of Nim, which is thoroughly explained in problem problem://problemsjutge.org:problems/upc/2004-semi1/5.pbm. 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 $10^9$ . Assume $0 \le n \le 10^5$ .

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:29:27.945Z