Problem: 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.

Input

The first line contains a single integer t (1≤ t≤ 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≤ n≤ 10^5) — the number of piles.

The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 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".

Example

Input


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


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 1 stone. The numbers of stones in piles will be [1, 5, 4]. 
  2. 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]. 
  3. 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]. 
  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]. 
  5. 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]. 
  6. The second player will lose the game because all piles will be empty. 

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.Scanner;

public class PilesGame {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = sc.nextInt();

            int k=0;
            while(k<n && a[k]==1)
                k++;

            if(k==n){
                if(n%2==0)
                    out.println("Second");
                else
                    out.println("First");
            }
            else{
                if(k%2==0)
                    out.println("First");
                else
                    out.println("Second");
            }
        }
        out.close();
    }
}
/*

B. Sequential Nim
time limit per test1 second
memory limit per test256 megabytes
inputstandard input
outputstandard output
There are n piles of stones, where the i-th pile has ai 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 t (1≤t≤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≤n≤105)  — the number of piles.

The second line of each test case contains n integers a1,…,an (1≤ai≤109)  — ai 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 105.

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

Example
inputCopy
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
outputCopy
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.
 */