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 MyClass {
    static int arr[];
    static int k;
    static void fac(int n)
    {
        int i;
        for(i=1;i<=Math.sqrt(n);i++)
            {
                if(n%i==0)
                {
                    if(n/i==i && i%2!=0)
                    arr[k++]=i;
                
                    else
                  {
                    if(i!=1 && i%2!=0) 
                    arr[k++]=i;
                    if((n/i)%2!=0)
                    arr[k++]=n/i;
                   }
                }
            }
    }
    public static void main(String args[]) {
    
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
        
            int i;
            
            int c=0;
            if(n==1)
            System.out.println("FastestFinger");
            else if(n==2)
            System.out.println("Ashishgup");
            else if(n%2!=0)
            System.out.println("Ashishgup");
            else
            {
            while(n>1)
            {
                arr=new int[1000000];
                k=0;
                fac(n);
                Arrays.sort(arr,0,k);
                k--;
                if(k>=0 && n/arr[k]==2)
                k--;
                if(k>=0 && n%arr[k]==0)
                {
                    n/=arr[k];
                    c++;
                }
                else
                {
                    n--;
                    c++;
                }
            }
            if(c%2==0)
            System.out.println("FastestFinger");
            else
            System.out.println("Ashishgup");
            }
            
            
        }
        sc.close();
    }
}