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.util.*;
public class Ishu
{
	public static void main(String[] args)
	{
	Scanner scan=new Scanner(System.in);
	int t,n,i;
	t=scan.nextInt();
	while(t-->0)
		{
		boolean flag=false;
		n=scan.nextInt();
		int N=n;
		while(N>1&&N%2==0)
			N/=2;
		if(N==1)
			flag=true;
		String ans="Ashishgup";
		if(n==1)
			ans="FastestFinger";
		else if(n==2);
		else if(flag)
			ans="FastestFinger";
		else if(n%2==0&&n%4!=0)
			{
			int ctr=0;
			n/=2;
			for(i=2;i*i<=n;++i)
				if(n%i==0)
					++ctr;
			if(ctr==0)
				ans="FastestFinger";
			}
		System.out.println(ans);
		}
	}
}
