Xormites

Consider the following two-player game on a sequence of $N$ integers. The two players move in turns. In each move, the current player selects a value that is either at the beginning or at the end of the sequence, adds it to their own XOR sum, and removes it from the sequence.

This is a well-known game. In this problem, however, the players add the values to a XOR sum instead of a regular sum. Initially, the XOR sums of both players are $0$. When adding a new value, the players use the bitwise XOR operation in place of addition.

The game ends when the sequence is empty. The player with the highest XOR sum wins, and the game may also end in a draw. Determine the outcome of the game when both players play optimally.

The first line contains an integer $T$, the number of test cases ($1 \le T \le 12$). Each test case starts with a line containing an integer $N$ ($1 \le N \le 50\,000$). The next line contains a sequence of $N$ positive integers ($1 \le X \le 10^9$ for every integer $X$ in the sequence).

Print $T$ lines, one per test case. The $i$-th line must contain the answer for the $i$-th test case. The answer must be one of the following:

• First if the first player to move wins.
• Second if the second player to move wins.
• Draw if the game ends in a draw.