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.*;
import java.util.*;
public class Graph
{
    static int countDivisors(int n) 
    { 
        int cnt = 0; 
        for (int i = 1; i <= Math.sqrt(n); i++) 
        { 
            if (n % i == 0) { 
                // If divisors are equal, 
                // count only one 
                if (n / i == i) 
                    cnt++; 
  
                else // Otherwise count both 
                    cnt = cnt + 2; 
            } 
        } 
        return cnt; 
    }
    public static void main (String[] args)throws java.lang.Exception {
        try{
        Scanner sc=new Scanner(System.in);
          int t=sc.nextInt();
          while(--t>=0)
          {
              long n=sc.nextLong();
              if(n==1)
              System.out.println("FastestFinger");
              else if(n%2!=0)
              System.out.println("Ashishgup");
              else
              {
                  int c=0;
                  while(n%2==0)
                  {
                      c=c+1;
                      n=n/2;
                  }
                  if(n>2){
                  if(c==1)
                  {
                    if(countDivisors((int)n)<=2)
                    System.out.println("FastestFinger");
                    else
                    System.out.println("Ashishgup");
                  }
                  else
                    System.out.println("Ashishgup");
                  }
                  else{
                      if(c==1)
                        System.out.println("Ashishgup");
                      else
                        System.out.println("FastestFinger"); 
                  }
              }
          }
        }catch(Exception e){
            return;
        }
    }
    
}