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 numberGame {
	public static Boolean isPrime(int n) {
		for(int i = 3;i*i <= n;i += 2)
		{
			if(n%i == 0)
				return false;
		}
		return true;
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int T = sc.nextInt();
		while(T-- > 0)
		{
			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
				{
					if((n/2)%2 == 1)
					{
						if(isPrime(n/2))
							System.out.println("FastestFinger");
						else
							System.out.println("Ashishgup");
					}
					else
					{
						while(n%2 == 0)
							n /= 2;
						if(n == 1)
							System.out.println("FastestFinger");
						else
							System.out.println("Ashishgup");
					}
				}
			}
		}
		sc.close();
	}

}
