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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static Scanner sc = new Scanner(System.in);
	public static StringTokenizer st;

	public static String win = "Ashishgup";
	public static String lose = "FastestFinger";

	public static void main(String[] args) throws IOException {
		int iter = Integer.parseInt(br.readLine());

		while (iter-- > 0) {
			solve();
		}
	}

	public static void solve() throws NumberFormatException, IOException {
		int num = Integer.parseInt(br.readLine());

		if (num == 1) {
			System.out.println(lose);
		} else if (num == 2) {
			System.out.println(win);
		} else if (num % 2 == 1) {
			System.out.println(win);
		} else if (Integer.bitCount(num) == 1) {
			System.out.println(lose);
		} else if (isPrime(num / 2)) {
			System.out.println(lose);
		} else {
			System.out.println(win);
		}
	}

	private static boolean isPrime(int num) {

		for (int i = 2; i * i <= num; i++) {
			if (num % i == 0) {
				return false;
			}
		}

		return true;
	}

}
