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 CF {

	
	static boolean Prime(long n)
	{
		for(int i=2;i<=Math.sqrt(n);i++)
		{
			if(n%i==0)
			{
				return false;
			}
		}
		return true;
	}
	

	
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

		int test=sc.nextInt();
		while(test-->0)
		{
			long n=sc.nextLong();
			boolean check=false;
			if(n==1)
			{
				System.out.println("FastestFinger");
			}
			else if(n==2 || n%2!=0)
			{
				System.out.println("Ashishgup");
			}
			else {
				if(n>2 && n%2==0)
				{
					if((n&(n-1))==0)
					{
						check=true;
					}
					if(n%4!=0 && Prime(n/2) )
					{
						check=true;
					}
				}
				if(check)
				{
					System.out.println("FastestFinger");
				}
				else {
					System.out.println("Ashishgup");
				}
				
			}
			
		
				
			
			
			
			
		}
				
	}
}
