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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class CF1370C {
    public static void main(String[] args) {
        FastReader input = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);



        int t = input.nextInt();
        while (t > 0){
            int n = input.nextInt();
            if(n == 1){
                pw.println("FastestFinger");
            }
            else if(n != 1 && n % 2 != 0){
                pw.println("Ashishgup");
            }
            else if(n == 2){
                pw.println("Ashishgup");
            }
            else if(n % 2 == 0 && n > 2){
                int x = 0;
                int y = 0;

                for(int i = 2;i <= Math.sqrt(n);i++){
                    if(n % i == 0){
                        while (n % i == 0){
                            n = n / i;
                            if(i == 2)
                                x++;
                            else
                                y++;
                        }
                    }
                }

                if(n == 2)
                    x++;
                if(n > 2)
                    y++;

               // System.out.println(x + " " + y);

                if(y == 0){
                    pw.println("FastestFinger");
                }
                else if(x == 1 && y == 1){
                    pw.println("FastestFinger");
                }
                else if(x > 1 && y >= 1){
                    pw.println("Ashishgup");
                }
                else if(x == 1 && y >= 1){
                    pw.println("Ashishgup");
                }
            }
            t--;
        }
        pw.flush();
        pw.close();
    }
    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;
        }
    }
}
