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.*;
import java.io.*;

public class Main {
	static class Reader {
		BufferedReader br; StringTokenizer st;

		public Reader() { br = new BufferedReader(new InputStreamReader(System.in)); }

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try { st = new StringTokenizer(br.readLine());
				} catch (IOException e) { e.printStackTrace(); }
			}
			return st.nextToken();
		}

		int nextInt() { return Integer.parseInt(next()); }
		long nextLong() { return Long.parseLong(next()); }
		double nextDouble() { return Double.parseDouble(next()); }
	}

	static boolean isPrime(int n) {
		int t = 1;
		int m = (int)(Math.sqrt(n));
		while (t++ <= m) {
			if (n % t == 0) return false;
		}
		return true;
	}

	public static void main(String[] args) {
		Reader r = new Reader();
		int t = r.nextInt();

		String[] win = {"Ashishgup", "FastestFinger"};

		while (t-- > 0) {
			int n = r.nextInt();
			
			int w = 0;
			if (n < 3) w = n % 2;
			else if (n % 2 == 1) w = 0;
			else if ((n & (n - 1)) == 0) w = 1;
			else if (n % 4 != 0 && isPrime(n / 2)) w = 1;

			System.out.println(win[w]);
		}

	}

}
