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.util.*;
import java.io.*;
public class SequentialNim 
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);

        int T;
        T=in.nextInt();
        while((T--)>0)
        {
            //code comes here
            int N=in.nextInt();
            int arr[]=new int[N];
            char starter[]=new char[N];
            char finisher[]=new char[N];
            for(int i=0;i<N;i++)
            {
                arr[i]=in.nextInt();
            }
            starter[N-1]='F';
            finisher[N-1]='F';
            for(int i=N-2;i>=0;i--)
            {
                if(arr[i]==1)
                {
                    if(starter[i+1]=='S')
                    {
                        starter[i]='F';
                        finisher[i]='F';
                    }
                    else
                    {
                        starter[i]='S';
                        finisher[i]='F';
                    }
                }
                else
                {
                    if(starter[i+1]=='F')
                    {
                        starter[i]='F';
                        finisher[i]='S';
                    }
                    else
                    {
                        starter[i]='F';
                        finisher[i]='F';
                    }
                }
            }
            if(starter[0]=='F')
            {
                out.println("First");
            }
            else
            {
                out.println("Second");
            }




        }   
        out.flush();
        in.close();
        out.close();
    }

    static void printSDA(int arr[])
    {
        int l=arr.length;
        for(int i=0;i<l;i++)
        {
            System.out.print(arr[i]+" ");
        }
    }

}