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 javafx.util.Pair;
import sun.java2d.loops.ProcessPath;
import sun.reflect.generics.tree.Tree;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;


public final class Main {

    public static void main(String[] args) {


        Scanner s = new Scanner(System.in);


        int TC = s.nextInt();

        out:for (int tc = 0; tc < TC; tc++) {

            int n = s.nextInt();

            if (n % 2 == 1 ) {


                if (n == 1)  System.out.println("FastestFinger");

                else System.out.println("Ashishgup");


            } else {

                if (n == 2) {

                    System.out.println("Ashishgup");

                    continue;
                }

                int k = n;

                while (k % 2 == 0) {

                    k = k /2;
                }

                if (k == 1) {

                    System.out.println("FastestFinger");
                } else {

                    if (k * 2 == n) {

                        for (int i = 3; i*i <= k; i+=2) {

                            if (k % i == 0) {

                                System.out.println("Ashishgup");

                                continue out;
                            }
                        }
                        System.out.println("FastestFinger");
                    } else {

                        System.out.println("Ashishgup");
                    }
                }
            }
        }
    }





}