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.*; 
public class C_651{
public static void main(String[] args)
{
   Scanner omkar = new Scanner(System.in);
   int cases = omkar.nextInt();
   for(int i = 0; i < cases; i++)
   {
      if(solve(omkar))
      {
         System.out.println("Ashishgup");
      }
      else
      {
         System.out.println("FastestFinger");
      }  
   }
   
      }
public static boolean solve(Scanner omkar)
{
   int num = omkar.nextInt(); 
   if(num == 2)
   {
      return true;
   }
   if(num == 1)
   {
      return false;
   }  
   if(num % 2 == 1)
   {
      return true;
   }
   if(isPrime(num/2))
   {
      return false;
   }
   while(num % 2 == 0)
   {
      num = num/2;   
   }
   if(num == 1)
   {
      return false;
   }
   return true;
}
public static boolean isPrime(int n)
{
   for(int i = 2; i <= (int)(Math.pow(n, 0.5)); i++)
   {
      if(n % i == 0)
      {
         return false;
      }
   }
   return true;
}
}