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.io.*;

public class C{
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public static void main (String[] args) throws IOException
	{
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
            int n = Integer.parseInt(br.readLine());
            if(n == 1){
                bw.write("FastestFinger");
                bw.newLine();
                continue;
            }
            if(n == 2){
                bw.write("Ashishgup");
                bw.newLine();
                continue;
            }
            if(n%2!=0){
                bw.write("Ashishgup");
                bw.newLine();
                continue;
            }
            if((n&(n-1)) == 0){
                bw.write("FastestFinger");
                bw.newLine();
                continue;
            }
            n = n/2;
            boolean prime = checkprime(n);
            if(prime){
                bw.write("FastestFinger");
                bw.newLine();
                continue;
            }else{
                bw.write("Ashishgup");
                bw.newLine();
                continue;
            }
        }
    bw.flush();
    }

    public static boolean checkprime(int n){
        boolean p = false;
        int c = 0;
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                c++;
            }
        }
        if(c==0){
            return true;
        }
        return p;
    }
}