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.*;
import java.math.*;
import java.util.*;

public class Sample
{

    static int[][][] dp;
    static int[] are;

    public static void main(String[] args) throws InterruptedException {
        Thread t=new Thread(null, null,"", 1<<28) {
            public void run() {
                m();
            }
        };
        t.start();
        t.join();
    }

    public static void m()
    {
        FastScanner in=new FastScanner();
        int t = in.nextInt();
        while(t-->0)
        {
            int n = in.nextInt();
            {
                if(n==1) System.out.println("FastestFinger");
                else if(n<3) System.out.println("Ashishgup");
                else if(n%2!=0) System.out.println("Ashishgup");
                else {
                    boolean check = false;
                    for (int i = 2; i * i <= n/2; i++) {
                        if ((n/2) % i == 0) {
                            check = true;
                        }
                    }
                    if ((n & (n - 1)) == 0) System.out.println("FastestFinger");
                    else if (!check) System.out.println("FastestFinger");
                    else System.out.println("Ashishgup");
                }
            }
        }
    }

/*
1
5
01101
10101

*/

    static void print(String[] are)
    {
        for(int i=0; i<are.length; i++)
            System.out.print(are[i]);
        System.out.println();
    }

    static void sort(int[] a)
    {
        ArrayList<Integer> list=new ArrayList<>();
        for (int i:a) list.add(i);
        Collections.sort(list);
        for (int i=0; i<a.length; i++) a[i]=list.get(i);
    }

    static class FastScanner
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");

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

        }

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

        public int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }

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

        public long[] readLongArray(int n) {
            long[] a=new long[n];
            for (int i=0; i<n; i++) a[i]=nextLong();
            return a;
        }
    }

}
