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 Main{
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			if(n==1) {
				System.out.println("FastestFinger");
				continue;
			}
			if(n==2) {
				System.out.println("Ashishgup");
				continue;
			}
			if(n%2==1) {
				System.out.println("Ashishgup");
				continue;
			}
			ArrayList<Integer> primes = primeFactors(n);
			int even=0,odd=0;
			for(int i : primes) {
				if(i%2==0)
					even++;
				else
					odd++;
			}
			if(odd==0) {
				System.out.println("FastestFinger");
			} else if(even>1) {
				System.out.println("Ashishgup");
			} else if(odd==1) {
				System.out.println("FastestFinger");
			} else {
				System.out.println("Ashishgup");
			}
		}
	}

	public static ArrayList<Integer> primeFactors(int n) {
		ArrayList<Integer> result = new ArrayList<>();
		while (n % 2 == 0) {
			result.add(2);
			n /= 2;
		}
		for (int i = 3; i <= Math.sqrt(n); i += 2) {
			while (n % i == 0) {
				result.add(i);
				n /= i;
			}
		}
		if (n > 2)
			result.add(n);
		return result;
	}
}
