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.ArrayList;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		int t=s.nextInt();
		
		for(int i=0;i<t;i++)
		{
			int n=s.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> list=primeFactors(n);
				
				int two=0;
				int count=0;
				
				for(int j=0;j<list.size();j++)
				{
					if(list.get(j)==2)
					{
						two++;
					}
				}
				
				for(int j=0;j<list.size();j++)
				{
					if(list.get(j)!=2)
					{
						count++;
					}
				}
				
				if(count+two>2&&count!=0)
				{
					System.out.println("Ashishgup");
				}
				else
				{
					System.out.println("FastestFinger");
				}
			}
			
		}
	}
	
	public static ArrayList primeFactors(int n) 
    { 
		ArrayList<Integer> list=new ArrayList<>();
		
        while (n%2==0) 
        { 
           list.add(2);
            n /= 2; 
        } 
  
        for (int i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            while (n%i == 0) 
            { 
               list.add(i);
                n /= i; 
            } 
        } 
  
        if (n > 2) 
        {
        	list.add(n);
        }
        
        return list;
    } 
	
}