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

        int t = sc.nextInt();
        for (int tc = 0; tc < t; ++tc) {
            int n = sc.nextInt();

            System.out.println(solve(n));
        }

        sc.close();
    }

    static String solve(int n) {
        boolean firstWin;
        if (n % 2 == 0) {
            int odd = n;
            while (odd % 2 == 0) {
                odd /= 2;
            }
            int even = n / odd;

            if (odd == 1) {
                firstWin = even == 2;
            } else {
                if (even == 2) {
                    firstWin = canFactorize(odd);
                } else {
                    firstWin = true;
                }
            }
        } else {
            firstWin = n != 1;
        }

        return firstWin ? "Ashishgup" : "FastestFinger";
    }

    static boolean canFactorize(int x) {
        for (int i = 2; i * i <= x; ++i) {
            if (x % i == 0) {
                return true;
            }
        }

        return false;
    }
}