Pebble Game

Two people sitting on the beach and looking out at the horizon decide to play a pebble game.

The game uses $N$ piles of pebbles. The $i$-th pile contains $A_i$ pebbles, and both players know the number of pebbles in every pile.

Starting with the first player, the two players take turns. On each turn, the current player must choose one pile containing at least three pebbles and split it into three piles. Each of the three new piles must contain at least one pebble, and the three piles may have equal sizes.

The opponent then chooses one of the three newly created piles to keep and removes the other two piles from the game. All piles that were not split remain unchanged. The opponent who chose which pile to keep then takes the next turn and splits a pile.

A player loses if, on their turn, no pile contains at least three pebbles. Assuming both players play optimally, determine who wins!

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

Each test case consists of two lines.

The first line contains the number of piles $N$.

The second line contains $N$ space-separated integers $A_1, A_2, \cdots, A_N$, representing the number of pebbles in each pile.

For each test case, print First if the first player wins, or Second if the second player wins. Print one answer per line.

• $1 \le T \le 10\,000$.
• $1 \le N \le 200\,000$.
• $1\le {}_{}$ ().