B. Sequential Nim

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There are nn piles of stones, where the ii-th pile has aiai 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.

Input

The first line contains a single integer tt (1≤t≤10001≤t≤1000)  — the number of test cases. Next 2t2t lines contain descriptions of test cases.

The first line of each test case contains a single integer nn (1≤n≤1051≤n≤105)  — the number of piles.

The second line of each test case contains nn integers a1,…,ana1,…,an (1≤ai≤1091≤ai≤109)  — aiai is equal to the number of stones in the ii-th pile.

It is guaranteed that the sum of nn for all test cases does not exceed 105105.

Output

For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".

Example

input

Copy

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

output

Copy

First
Second
Second
First
First
Second
First

Note

In the first test case, the first player will win the game. His winning strategy is:

1. The first player should take the stones from the first pile. He will take 11 stone. The numbers of stones in piles will be [1,5,4][1,5,4].
2. The second player should take the stones from the first pile. He will take 11 stone because he can't take any other number of stones. The numbers of stones in piles will be [0,5,4][0,5,4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 44 stones. The numbers of stones in piles will be [0,1,4][0,1,4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 11 stone because he can't take any other number of stones. The numbers of stones in piles will be [0,0,4][0,0,4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 44 stones. The numbers of stones in piles will be [0,0,0][0,0,0].
6. The second player will lose the game because all piles will be empty.

解题说明：此题是一道博弈问题，经过分析能发现。所以碰到a[i]>1时,此时先手的人必胜。碰到a[i]==1时,改变先后手情况。

#include
int main()
{
	long int t,i,j,n,c,a[100000];
    scanf("%ld",&t);
    for(i=0;i