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 Test {

    public static boolean prime(long n){
        for(int i = 2 ; i <= Math.sqrt(n);i++){
            if(n % i == 0){
                return false;
            }
        }
        return true;
    }

    public static void solve(long n){
        String one = "Ashishgup";
        String two = "FastestFinger";
        if(n == 1){
            System.out.println(two);
            return;
        }
        if(n==2){
            System.out.println(one);
            return;
        }
        if(n % 2 == 1){
            System.out.println(one);
        }
        else{
            long times = 0;
            while(n % 2 == 0){
                n /= 2;
                times++;
            }
            if(times == 1){
                if(prime(n)){
                    System.out.println(two);
                }
                else{
                    System.out.println(one);
                }
            }
            else if(times > 1){
                if(n==1){
                    System.out.println(two);
                }
                else{
                    System.out.println(one);
                }
            }
        }
    }

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int t = sc.nextInt();

        while(t > 0){
            t--;
            long n = sc.nextLong();
            solve(n);
        }

    }

}
