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.util.*;
import java.util.Scanner;

/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

public class Main {
   static int N = 50000;
   public static void main(String[] args) {
      // Write your solution here
      Scanner in = new Scanner(System.in);
      int t = in.nextInt();
      while(t != 0){
         int n = in.nextInt();
         boolean AshishLost = (n == 1);
         if(n > 2 && n % 2 == 0){
            if((n & (n - 1)) == 0){
               AshishLost = true;
            } else if(n % 4 !=0 && isPrime(n / 2)){
               AshishLost = true;
            }
         }
         if(AshishLost){
            System.out.println("FastestFinger");
         } else {
            System.out.println("Ashishgup");
         }
         t--;
      }
   }
   public static boolean isPrime(int n){
      for(int i = 2; i < Math.min(n, N); i++){
         if(n % i == 0){
            return false;
         }
      }
      return true;
   }
}