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;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(reader.readLine());
        StringBuilder ans = new StringBuilder();
        while (t-->0) {
            int n = Integer.parseInt(reader.readLine());
            if (n==1) ans.append("FastestFinger\n");
            else if (n==2) ans.append("Ashishgup\n");
            else if (n==4) ans.append("FastestFinger\n");
            else if (n==6) ans.append("FastestFinger\n");
            else {
                if (n%2==1) ans.append("Ashishgup\n");
                else {
                    if (n%2==0 && (n/2)%2==1) {
                        n = n/2;
                        int res = 0;
                        for (int i=3; i<(int) Math.sqrt(n)+2; i++) {
                            if (n%i==0) {
                                res = 1; break;
                            }
                        }
                        if (res==0) ans.append("FastestFinger\n");
                        else ans.append("Ashishgup\n");
                    } else {
                        int res = 0;
                        for (int i=2; i<(int) Math.sqrt(n)+2; i++) {
                            if (n%i==0) {
                                if (i%2==1 || (n/i)%2==1) {
                                    res = 1; break;
                                }
                            }
                        }
                        if (res==0) ans.append("FastestFinger\n");
                        else ans.append("Ashishgup\n");
                    }
                }
            }
        }
        System.out.println(ans);
    }
}