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.io.*;
import java.util.*;

public class C 
{
	 
	public static void main(String[] args)throws IOException 
	{	
		BufferedReader ob=new BufferedReader(new InputStreamReader(System.in));
		StringBuffer sb=new StringBuffer();
		
		int test=Integer.parseInt(ob.readLine());
		
		while(test-->0)
		{
			int n=Integer.parseInt(ob.readLine());
			
			if(n==1)
			{
				sb.append("FastestFinger\n");
				continue;
			}
			if(n%2!=0 || n==2)
			{
				sb.append("Ashishgup\n");
				continue;
			}
			
			int nf[]=primeFactors(n);
			
			int ev=nf[0];
			int od=nf[1];
//			System.out.println("ev = "+ev);
//			System.out.println("od = "+od);
			if(od==0 || (od==1 && ev==1))
			{	
				sb.append("FastestFinger\n");
				continue;
			}
			else
			{
				sb.append("Ashishgup\n");
			}
		}
		System.out.println(sb);
		
	}
	static int[] primeFactors(int n) 
	{	
		// a[0] => ev
		// a[1] => odd
		int a[]=new int[2];
		int count = 0;
		for (int i = 2; i <= Math.sqrt(n); i++) {
			if (n % i == 0) {
				count = 0;
				while (n % i == 0) {
					n /= i;
					count++;
				}
				if (count > 0)
				{	
					if(i%2==0)
						a[0]+=count;
					else
						a[1]+=count;	
				}	
			}
		}
		if (n > 1)
			a[1]++;

		return a;
	}
}
