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 NumberGame {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while (t > 0) {
            int n = in.nextInt();

            if (n == 2)
                System.out.println("Ashishgup");
            else if (n == 1 || (n & (n - 1)) == 0)
                System.out.println("FastestFinger");
            else if ((n & 1) == 1)
                System.out.println("Ashishgup");
            else if (n % 4 == 0 || !isPrime(n / 2))
                System.out.println("Ashishgup");
            else
                System.out.println("FastestFinger");
            t--;
        }
    }

    private static boolean isPrime(int n) {
        if ((n & 1) != 1)
            return false;
        for (long i = 3; i * i <= n; i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

}
