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 Question3 {
static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		int t = sc.nextInt();
		while(t-->0) {
			solve();
		}
	}
	
	public static void solve() {
		int n = sc.nextInt();
		if(n == 1) {
			System.out.println("FastestFinger");
		}
		else if(n == 2)System.out.println("Ashishgup");
		else if(n % 2 == 1) {
			System.out.println("Ashishgup");
		}
		else {
			findFactor(n);
		}
	}
	
	public static void findFactor(int n) {
		
		int twos = 0; int other = 0;
		
		while(n % 2 == 0) {
			n = n/2;
			twos++;
		}
		
		int i = 3;
		while(i <= (int)Math.sqrt(n)) {
			if(n % i == 0) {
				n = n/i;
				other++;
			}else i++;
		}
		
		if(n > 1) {
			other ++;
			
		}
		
		findAnswer(twos, other);
	}
	
	public static void findAnswer(int twos, int others) {
		if(others == 0) {
			System.out.println("FastestFinger");
		}
		
		else if(twos == 1 && others == 1) {
			System.out.println("FastestFinger");
			
		}
		
		else {
			System.out.println("Ashishgup");
		}
	
	}
}
