Description

Alice and Bob, two good friends, are playing a stone-taking game again. At the beginning of the game, there are $N$ piles of stones arranged in a row. They take turns to make moves (Alice goes first), and in each move, they can choose one of the following rules:

• Take one stone from any pile;
• Merge any two piles of stones.

The player who cannot make a move loses. Alice wants to know if she has a winning strategy.

Input Format

The first line contains $T$, the number of test cases.

For each test case, the first line contains $N$;
The next $N$ positive integers $a_1, a_2, \cdots, a_n$ represent the number of stones in each pile.

Output Format

For each test case, output one line.

Output YES if Alice has a winning strategy, and NO otherwise.

Sample 1

3
3
1 1 2
2
3 4
3
2 3 5

YES
NO
NO

Constraints & Notes

For all test cases, $T\le 100, N\le 50, a_i\le 1000$.