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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Q3 {
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		MScanner s = new MScanner(System.in);
		int t = s.nextInt();
		while (t-- > 0) {
			int n = s.nextInt();
			if (n == 1) {
				System.out.println("FastestFinger");
				continue;
			}
			if (n == 2 || n % 2 != 0) {
				System.out.println("Ashishgup");
				continue;
			}
			int even = 0;
			int odd = 0;
			while (n % 2 == 0) {
				even++;
				n /= 2;
			}
			for (int i = 3; i <= Math.sqrt(n); i++) {
				while (n % i == 0) {
					odd++;
					n = n / i;
				}
			}
			if (n > 2) {
				odd++;
			}
			if (odd > 0 && even >= 2) {
				System.out.println("Ashishgup");
			} else if (odd >= 2 && even == 1) {
				System.out.println("Ashishgup");
			} else {
				System.out.println("FastestFinger");
			}
		}

	}

	static class MScanner {
		StringTokenizer st;
		BufferedReader br;

		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int[] intArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public long[] longArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public int[] intSortedArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public long[] longSortedArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public Integer[] IntegerArr(int n) throws IOException {
			Integer[] in = new Integer[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public Long[] LongArr(int n) throws IOException {
			Long[] in = new Long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}

	}

	static void shuffle(int[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			int tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}

	static void shuffle(long[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			long tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}
}