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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(bf.readLine());
	while(t-->0)
	{
	    int n=Integer.parseInt(bf.readLine());
	    if(n==1)
	    {
	        System.out.println("FastestFinger");
	    }
	    else if(n==2)
	    {
	        System.out.println("Ashishgup");
	    }
	    else if(n==3)
	    {
	        System.out.println("Ashishgup");
	    }
	    else
	    {
	        if(n%2==0)
	        {
	            int z=divisor(n);
	    //        System.out.println("z "+z);
	            if(z>=2)
	            {
	                 System.out.println("Ashishgup");
	            }
	            else
	            {
	                if(z==0)
	                {
	                    System.out.println("FastestFinger");
	                }
	                else if(z==1)
	                {
	                    int count=0;
	                    while(n%2==0)
	                    {
	                        count++;
	                        n=n/2;
	                    }
	                    if(count==1)
	                    System.out.println("FastestFinger");
	                    else
	                    System.out.println("Ashishgup");
	                }
	            }
	            
	          
	            
	        }
	        else
	        {
	            System.out.println("Ashishgup");
	        }
	        
	    }
	   
	}
	
	}
public static int divisor(int n)
{
    ArrayList<Integer> hs=new ArrayList<>();
   // int z=n/2;
 //   int count=0;
    for(int i=2;i<=Math.sqrt(n);i++)
    {
        if(n%i==0)
        {
            if(i%2!=0)
            hs.add(i);
            int z=n/i;
            if(z%2!=0)
            {
                hs.add(z);
            }
           
        }
    }
    return hs.size();
}
	
}