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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * I realized that you might have doubt in this question, so if at some point in my 
 * code you find anything that you don't understand, please do not disturb me.
 *
 *                                                                 - Sheldon Cooper
 */

public class Sheldon {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter pw = new PrintWriter(System.out);
        
        try {
            int t = Integer.parseInt(br.readLine());
            while(t-->0) {
                int n = Integer.parseInt(br.readLine());
                if(n == 1) {
                    pw.println("FastestFinger");
                }
                else if(n == 2) {
                    pw.println("Ashishgup");
                }
                else if(n%2 == 1) {
                    pw.println("Ashishgup");
                }
                else {
                    int x = n;
                    while(x%2 == 0) x/=2;
                    if(x == 1) {
                        pw.println("FastestFinger");
                    }
                    else {
                        if(n/2%2 == 0) {
                            pw.println("Ashishgup");
                        }
                        else {
                            int rem = n/2;
                            boolean div = true;
                            for(int i=2 ; i*i<=rem ; i++) {
                                if(rem%i == 0) {
                                    div = false;
                                    break;
                                }
                            }

                            if(div) {
                                pw.println("FastestFinger");
                            }
                            else {
                                pw.println("Ashishgup");
                            }
                        }
                    }
                }
            }
        }
        finally {
            pw.flush();
            pw.close();
        }
    }
}
