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.Scanner;


public class SequentialNim {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);
		int T = sc.nextInt();
		while(T-->0){
			int n = sc.nextInt();
			int[] arr = new int[n];
			int one = 0;
			String winner = "First";
			int r = 0;
			for(int i=0;i<n;i++){
				int num = sc.nextInt();
				arr[i] = num;
				if(num == 1){
					one++;
				}
			}
			if(one == 0){
				System.out.println("First");
			}
			else if(one == n){
				if(n%2 == 0)
					System.out.println("Second");
				else
					System.out.println("First");
			}
			else if(one==1 && arr[0] == 1)
				System.out.println("Second");
			else if(one == 1){
				System.out.println("First");
			}
			else{
				int i=0;
//				while(i<n){
					int c = 0;
					for(;i<n;i++){
						if(arr[i] == 1)
							c++;
						else{
							i++;
							break;
						}
					}
					if(c%2==0){}
					else{
						if(winner.equals("First"))
							winner = "Second";
						else
							winner ="First";
					}
//				}
				System.out.println(winner);
			}
		}
	}

}