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.ArrayList;
import java.util.List;
import java.util.Scanner;

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

        for (int t = 0; t < test; t++) {
            int n = scanner.nextInt();
            scanner.nextLine();
            boolean result = calculateResult(n);
            System.out.println(result ? "Ashishgup" : "FastestFinger");

        }
    }

    static Integer[] factorsOf(int val) {
        List<Integer> numArray = new ArrayList<Integer>();

        for (int i = 2; i <= Math.ceil(Math.sqrt(val)); i++) {
            if (val % i == 0) {
                numArray.add(i);
                val /= i;
            }
        }
        numArray.add(val);
        return numArray.toArray(new Integer[numArray.size()]);
    }

    public static boolean calculateResult(int n) {
        if (n == 1) {
            return false;
        } else if (n == 2) {
            return true;
        }

        if (n % 2 == 1) {
            return true;
        }

        int num = n;
        int x = 0;
        while (num % 2 == 0) {
            num /= 2;
            x++;
        }

        if (num == 1) {
            return false;
        }

        if (x > 1) {
            return true;
        }

        Integer[] integers = factorsOf(num);
        if (integers.length > 1) {
            return true;
        }
        return false;
    }
}
