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.*;
import java.lang.*;
import java.io.*;
public class Main
{
    public static boolean check(long n) 
    { 
        if(n<2) 
        return false; 
        if(n<4) 
        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
	{
		Scanner sc=new Scanner(System.in);
		int test=sc.nextInt();
		while(test-->0)
		{
		    long n=sc.nextLong();
		    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 if((n&(n-1))==0)
		        System.out.println("FastestFinger");
		        else
		        {
		            if(check(n/2))
		            System.out.println("FastestFinger");
		            else
		            System.out.println("Ashishgup");
		        }
		    }
		}
	}
}