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.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        FastReader s = new FastReader();
        int T = s.nextInt();
        int n;
        while (T-- > 0) {
            n=s.nextInt();
            if((n%2!=0 &&n>1) || n==2 )
                System.out.println("Ashishgup");
            else{
                if((n&(n-1))==0){
                    System.out.println("FastestFinger");
                    continue;
                }
                if((n%4)==0){
                    System.out.println("Ashishgup");
                    continue;
                }
                int odd =0 ;
                for (int i = 2; i * i <= n; ++i)
                {
                    if (n % i!=0) continue;
                    while ((n % i)==0)
                    {
                        n /= i;
                        odd += i & 1;
                    }
                }
                if(n>1)
                    odd++;
                if (odd > 1)
                    System.out.println("Ashishgup");
                else
                    System.out.println("FastestFinger");
            }
        }
    }

    private static boolean isPrime(int n) {
        if (n == 2)
            return true;
        else if ((n % 2 == 0 && n > 2) || n < 2)
            return false;
        else {
            for (int i = 3; i <= (int) Math.sqrt(n); i += 2) {
                if (n % i == 0)
                    return false;
            }
            return true;
        }


    }

    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;
        }
    }

}