Ashishgup and FastestFinger play a game. 

They start with a number n and play in turns. In each turn, a player can make any one of the following moves:

  * Divide n by any of its odd divisors greater than 1. 
  * Subtract 1 from n if n is greater than 1. 



Divisors of a number include the number itself.

The player who is unable to make a move loses the game.

Ashishgup moves first. Determine the winner of the game if both of them play optimally.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer — n (1 ≤ n ≤ 10^9).

Output

For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).

Example

Input


7
1
2
3
4
5
6
12


Output


FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

Note

In the first test case, n = 1, Ashishgup cannot make a move. He loses.

In the second test case, n = 2, Ashishgup subtracts 1 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the third test case, n = 3, Ashishgup divides by 3 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the last test case, n = 12, Ashishgup divides it by 3. Now n = 4, FastestFinger is forced to subtract 1, and Ashishgup gets 3, so he wins by dividing it by 3.
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Scanner;

public class NumberGame {

	
	public static void main(String[] args){
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int T = s.nextInt();
		while(T>0)
		{
			int n = s.nextInt();
			if(n == 1)
			{
				System.out.println("FastestFinger");
				T--;
				continue;
			}
			if(n==2)
			{
				System.out.println("Ashishgup");
				T--;
				continue;
			}
			if(n%2 == 1)
			{
				System.out.println("Ashishgup");
			}
			else
			{
				int e = 0,o=0;
				int p = (int)Math.sqrt(n);
				for(int i = 2;i<=p && n>1;i++)
				{
					if(i == 2)
					{
						while(n%i == 0)
						{
							n = n/i;
							e++;
						}
					}
					else
					{
						while(n%i == 0)
						{
							n = n/i;
							o++;
						}
					}
				}
				if(n>2)
					o++;
				if(o == 0 || (e==1 && o==1))
				{
					System.out.println("FastestFinger");
				}
				else
					System.out.println("Ashishgup");
					
			}
			T--;
		}

	}

}
