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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public final class C {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int t = Integer.parseInt(in.nextLine());
        for (int x = 0; x < t; x++) {
            final int n = Integer.parseInt(in.nextLine());
            System.out.println(dfs(n) ? "FastestFinger": "Ashishgup");
        }
    }

    private static boolean dfs(int n) {
        if (n == 1) {
            return true;
        }
        if (n % 2 != 0) {
            return false;
        }
        int divMax = -1;
        int divMin = Integer.MAX_VALUE;
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                if ((n / i) % 2 != 0) {
                    divMax = Math.max(divMax, n / i);
                    divMin = Math.min(divMin, n / i);
                }
                if (i % 2 != 0) {
                    divMax = Math.max(divMax, i);
                    divMin = Math.min(divMin, i);
                }
            }
        }
        if (divMax == -1) {
            return !dfs(n - 1);
        } else {
            if (n % 4 != 0 && divMax != divMin) {
                return !dfs(n / (divMax / divMin));
            }
            return !dfs(n / divMax);
        }
    }
}
