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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author shwe
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CNumberGame solver = new CNumberGame();
        solver.solve(1, in, out);
        out.close();
    }

    static class CNumberGame {
        final int M = 50000;

        private boolean isPrime(int n) {
            for (int i = 2; i < Math.min(n, M); i++) {
                if (n % i == 0) {
                    return false;
                }
            }
            return true;
        }

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int t = Integer.parseInt(in.nextLine());
            for (int _ = 0; _ < t; _++) {
                int n = in.nextInt();
                boolean lose = n == 1;
                if (n > 2 && n % 2 == 0) {
                    if ((n & (n - 1)) == 0) {
                        lose = true;
                    } else if (n % 4 != 0 && isPrime(n / 2)) {
                        lose = true;
                    }


                }
                if (!lose)
                    out.println("Ashishgup");
                else
                    out.println("FastestFinger");

            }
        }

    }
}

