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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Task3 {

    public static void main(String[] args) throws IOException {
        new Task3().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int t = Integer.parseInt(f.readLine());
        for (int t1 = 0; t1 < t; t1++) {
            int n = Integer.parseInt(f.readLine());
            if (n == 1) {
                out.println("FastestFinger");
                continue;
            }
            if (n == 2) {
                out.println("Ashishgup");
                continue;
            }
            if (n % 2 == 1 && n > 1) {
                out.println("Ashishgup");
                continue;
            }

            int numberOfNotOddDivisors = 0;
            while (n % 2 == 0) {
                numberOfNotOddDivisors++;
                n /= 2;
            }
            if (n == 1) {
                out.println("FastestFinger");
                continue;
            }

            boolean isPrime = true;
            for (int i = 2; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    isPrime = false;
                }
            }

            if (numberOfNotOddDivisors > 1 || !isPrime) {
                out.println("Ashishgup");
                continue;
            }

            out.println("FastestFinger");
        }

        out.close();
    }
}
