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.

//devanshjsr

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

public class Solution
{
    
    static boolean isp(int n) 
    {  
        if(n==1)
        {
            return false;
        }
        
        if (n <= 3) 
            return true; 
  
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
  
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
  
        return true; 
    } 

    
	public static void main (String[] args) throws java.lang.Exception
	{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    StringTokenizer st=new StringTokenizer(br.readLine());
	       
		        int t=Integer.parseInt(st.nextToken());
		        
		        while(t>0)
		        {
		            st=new StringTokenizer(br.readLine());
		            int n=Integer.parseInt(st.nextToken());
		            
		            
		            if(n%2==1)
		            {
		                if(n==1)
		                {
		                    System.out.println("FastestFinger");
		                }
		                else
		                {
		                   System.out.println("Ashishgup"); 
		                }
		                
		            }
		            else
		            {
		                int c=0;
		                
		                if(n==2)
		                {
		                    System.out.println("Ashishgup");
		                    t--;
		                    continue;
		                }
		                
		                while(n%2==0 && n>1)
		                {
		                    c++;
		                    n=n/2;
		                }
		                
		                if(c==1)
		                {
		                    
		                    if(isp(n) || n==1)
		                    {
		                        System.out.println("FastestFinger");
		                    }
		                    else
		                    {
		                        System.out.println("Ashishgup");
		                    }
		                    
		                }
		                else
		                {
		                    if(n==1)
		                    {
		                        System.out.println("FastestFinger");
		                    }
		                    else
		                    {
		                        System.out.println("Ashishgup");
		                    }
		                    //System.out.println("Ashishgup");
		                }
		            }
		            
		            
		            t--;
		        }
		        
		        
		        
		     
	}
}