This is another problem about the game of Nim, which is thoroughly explained in problem P17438: “The game of Nim”. 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++