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.io.*;

public class Template {
	
	static Scanner sc = new Scanner(System.in);
	

	public static void main(String[] args) {
		int test = sc.nextInt();
		while(test-->0) {
			int n = sc.nextInt();
			System.out.println(func(n));
		}
	}
	
	public static String func(int n) {
		int temp = n;
		if(n==1) return "FastestFinger";
		if(n==2) return "Ashishgup";
		
		if(n%2==0) {
			while(temp%2==0) temp/=2;
			if(temp==1 || prime(n/2)) return "FastestFinger";
		}
		return "Ashishgup";
	}
	
	public static boolean prime(int n) {
		for(int i=2 ; i<=Math.sqrt(n) ; i++) {
			if(n%i==0) return false;
		}
		return true;
	}
	
	
	public static int[] readArray(int n) {
		int[] a = new int[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = sc.nextInt();
		}return a;
	}

}