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. Furthermore, now we assume that the player to make the last move loses, instead of winning.

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 ≤ n ≤ 10^{5}.
At least one set has one or more marbles.

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.

Public test cases

**Input**

6 1 1 0 0 5 0 1 2 4 0 3 3 0 5 1000 43210 17 123456 42 5 1000 43210 17 43801 42 4 1 1 1 1

**Output**

winning winning losing winning losing winning

Information

- Author
- Salvador Roura
- Language
- English
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++