Sequential Nim
Description
There are $n$ piles of stones, where the $i$-th pile has $a_i$ stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
The first line contains a single integer $t$ ($1\le t\le 1000$) — the number of test cases. Next $2t$ lines contain descriptions of test cases.
The first line of each test case contains a single integer $n$ ($1\le n\le 10^5$) — the number of piles.
The second line of each test case contains $n$ integers $a_1,\ldots,a_n$ ($1\le a_i\le 10^9$) — $a_i$ is equal to the number of stones in the $i$-th pile.
It is guaranteed that the sum of $n$ for all test cases does not exceed $10^5$.
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Input
The first line contains a single integer $t$ ($1\le t\le 1000$) — the number of test cases. Next $2t$ lines contain descriptions of test cases.
The first line of each test case contains a single integer $n$ ($1\le n\le 10^5$) — the number of piles.
The second line of each test case contains $n$ integers $a_1,\ldots,a_n$ ($1\le a_i\le 10^9$) — $a_i$ is equal to the number of stones in the $i$-th pile.
It is guaranteed that the sum of $n$ for all test cases does not exceed $10^5$.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Samples
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
- The first player should take the stones from the first pile. He will take $1$ stone. The numbers of stones in piles will be $[1, 5, 4]$.
- The second player should take the stones from the first pile. He will take $1$ stone because he can't take any other number of stones. The numbers of stones in piles will be $[0, 5, 4]$.
- The first player should take the stones from the second pile because the first pile is empty. He will take $4$ stones. The numbers of stones in piles will be $[0, 1, 4]$.
- The second player should take the stones from the second pile because the first pile is empty. He will take $1$ stone because he can't take any other number of stones. The numbers of stones in piles will be $[0, 0, 4]$.
- The first player should take the stones from the third pile because the first and second piles are empty. He will take $4$ stones. The numbers of stones in piles will be $[0, 0, 0]$.
- The second player will lose the game because all piles will be empty.