Playing With Stones

You and a friend play a game in which you take turns removing stones from piles. Initially there are $N$ piles containing $a_1, a_2, a_3, \ldots, a_N$ stones. On each turn, a player must choose one pile and remove at least one stone from it, but no more than half of that pile's current number of stones (that is, at most $\lfloor a_i / 2 \rfloor$ stones). A player who cannot make any move loses.

For example, with three piles of $5$, $1$, and $2$ stones, a player may take $1$ or $2$ stones from the first pile, cannot take anything from the second pile, and may take only $1$ stone from the third pile. No stone can be taken from the second pile because $1$ is more than half of $1$ (the size of that pile).

Assume both players play optimally and you move first. Determine whether you have a winning move. You have a winning move if, after making it, you can eventually win no matter how your friend responds.

The first line contains an integer $T$ ($T \le 100$), the number of test cases. Each test case begins with a line containing an integer $N$ ($1 \le N \le 100$), the number of piles. The next line contains $N$ integers $a_1, a_2, a_3, \ldots, a_N$ ($1 \le a_i \le 2 \times 10^{18}$), the number of stones in each pile.

For each test case, print "YES" if you have a winning move, or "NO" if you do not.