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 aaaaaaaa {
	public void run() throws Exception {
		FastReader file = new FastReader();
		int times = file.nextInt();
		for (int asdf = 0; asdf < times; asdf++) {
			int n= file.nextInt();
			if (n == 1) System.out.println("FastestFinger");
			else if (n == 2) System.out.println("Ashishgup");
			else if (n % 2 == 1) System.out.println("Ashishgup");
			else {
				TreeMap<Integer, Integer> pm = new TreeMap();
				int cur = n;
				while (cur % 2 == 0) {
					pm.putIfAbsent(2, 0);
					pm.put(2, pm.get(2) + 1);
					cur /= 2;
				}
				if (pm.get(2) != null && pm.get(2) > 1 && cur > 1) System.out.println("Ashishgup");
				else if (pm.get(2) != null && pm.get(2) == 1 && cur > 1) {
					if (isPrime(cur)) System.out.println("FastestFinger");
					else System.out.println("Ashishgup");
				}
				else System.out.println("FastestFinger");
			}
		}
		
	}
	public static boolean isPrime(int n) {
		for (int i= 2; i <= Math.sqrt(n); i++) {
			if (n % i== 0) return false;
		}
		return true;
	}
	public static void main(String[] args) throws Exception {
		new aaaaaaaa().run();
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			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());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}
