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.util.*;

public class Main
{
    public static void main(String args[]) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = Integer.parseInt(br.readLine());
        while(t-->0)
        {
            int n = Integer.parseInt(br.readLine());
            // String s1[] = br.readLine().trim().split(" ");
            // int n = Integer.parseInt(s1[0]);
            // int s = Integer.parseInt(s1[1]);
            // int a[] = new int[2*n];
            // for(int i = 0; i < 2*n; i++)
            //     if(Integer.parseInt(s1[i])%2 == 0)
            int k = 1;
            if(n == 1)
            {
                bw.write("FastestFinger"+"\n");
                continue;
            }
            if(n == 2)
            {
                bw.write("Ashishgup"+"\n");
                continue;
            }
            if(n%2 == 1)
            {
                bw.write("Ashishgup"+"\n");
                continue;
            }
            while(n > 0 && n%2 == 0)
            {
                n /= 2;
                k = k*2;
            }
            if(n > 1 && k > 2)
            {
                bw.write("Ashishgup"+"\n");
                continue;
            }    
            int f = 0;
            for(int i = 3; i*i <= n; i++)
                if(n%i == 0)
                    f = 1;
            if(f == 1)
            {
                bw.write("Ashishgup"+"\n");
                continue;
            }
            
            bw.write("FastestFinger"+"\n");
            continue;   
        }
        bw.flush();
    }
}