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.Scanner;

public class C {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();

        while(N-- > 0) {
            int n = scanner.nextInt();
            if(n==1) System.out.println("FastestFinger");
            else if(n==2) System.out.println("Ashishgup");
            else if(n%2==1) System.out.println("Ashishgup");
            else if((n&(1-n)) == n) System.out.println("FastestFinger");
            else if(n%4 == 0) System.out.println("Ashishgup");
            else if( isPrime(n/2) ) System.out.println("FastestFinger");
            else System.out.println("Ashishgup");
        }
    }

    public static boolean isPrime(int num){
        if ( num > 2 && num%2 == 0 ) {
            return false;
        }
        int top = (int)Math.sqrt(num) + 1;
        for(int i = 3; i < top; i+=2){
            if(num % i == 0){
                return false;
            }
        }
        return true;
    }
}
