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.Scanner;

public class Codeforces {
    static int temp;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		 Scanner in = new Scanner(System.in);
	        int t = in.nextInt();
	        while(t-->0) {
	        	int n = in.nextInt();
	        	temp =n;
                int win = 2;
                while(canMove(n)!=n){
                	if(win==2)
                		win =1;
                	else
                		win =2;
                	n= temp;
                }
	        	
                if(win==1)
	        	  System.out.println("Ashishgup");
                else
                  System.out.println("FastestFinger");	
	        }

	}
	
	static int canMove(int n){
		int re =n;
		if(n==1) re = n;
		else if(n%2!=0) re= 1;
		else {
			int max =0;
			for(int i =3; i<Math.sqrt(n); i++) {
				if(n%i==0) {
					int b = n/i;
					if(i%2!=0)
						max = Math.max(max, i);
					if(b%2!=0)
						max = Math.max(max, b);
				}
			}
			if(max!=0)
				re = n/max;
			else 
				re = n-1;
		}
		temp =re;
		return re;
	}
	
	
	static int gcd(int a, int b) 
	    { 
	      if (b == 0) 
	        return a; 
	      return gcd(b, a % b);  
	    }

}
