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.
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class S {
	public static void main (String[] args) {
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		l:while(t--!=0)
		{
		    int n=in.nextInt();
		    if(n==1)System.out.println("FastestFinger");
		    else if(n==2)System.out.println("Ashishgup");
		    else if(n%2!=0)System.out.println("Ashishgup");
		    else
		    {
		        ArrayList<Integer> al=new ArrayList<>();
		        for(int i=2;i*i<=n;i++)
		        {
		            if(n%i==0)
		            {
		                if(n/i==i && i%2!=0)al.add(i);
		                else 
		                {
		                    if(i%2!=0)
		                        al.add(i);
		                    if((n/i)%2!=0)      
		                        al.add(n/i);
		                }
		            }
		        }
		        Collections.sort(al,Collections.reverseOrder());
		        for(int i=0;i<al.size();i++)
		        {
		            int z=n/al.get(i);
		            if(z!=2)
		            {
		                System.out.println("Ashishgup");
		                continue l;
		            }
		        }
		        System.out.println("FastestFinger");
		    }
		}
	}
}