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.
//https://codeforces.com/problemset/problem/1370/C
//C. Number Game
import java.util.*;
import java.io.*;
public class CF_1370_C{

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

	public static void main(String[] args) throws Exception{		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
		StringBuilder sb = new StringBuilder();
		StringTokenizer st;

		int t = Integer.parseInt(br.readLine());
		while(t-->0){
			int n = Integer.parseInt(br.readLine());

			if(n==1)
				sb.append("FastestFinger");
			else if(n==2)
				sb.append("Ashishgup");
			else if(n%2==1)
				sb.append("Ashishgup");
			else{
				int temp = n;
				while(temp%2==0)
					temp/=2;
				if(temp==1)
					sb.append("FastestFinger");
				else{
					if(isPrime(n/2))
						sb.append("FastestFinger");
					else
						sb.append("Ashishgup");
				}
			}
			sb.append("\n");
		}

		pw.print(sb);
		pw.flush();
		pw.close();
	}
}