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.*;
public class Main {
    public static void main(String args[]) {
        Scanner scanner=new Scanner(System.in);
        int t=scanner.nextInt();
        while(t>0){
            String ans="";
            int temp=0;
            int n=scanner.nextInt();
            if(n==1) ans="FastestFinger";
            else if(n%2!=0 || n==2) ans="Ashishgup";
            else{
                for(int i=3;i*i<=n;i++){
                    if(n%i==0 && i%2!=0){
                        temp=i;
                    }
                    if(n%i==0 && n/i>i && (n/i)%2!=0){
                        temp=n/i;
                    }
                }
                if(temp==2 || temp==0) ans="FastestFinger";
                else ans="Ashishgup";
            }
            System.out.println(ans);
            t-=1;
        }
      
    }
}