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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.TreeSet;

public class Main {
	
	public static void main(String[] args) throws IOException {
		Scanner s = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String[] input;
		int t = Integer.parseInt(reader.readLine());
		while(t-->0) {
			int n = Integer.parseInt(reader.readLine());
			boolean odd = n % 2 == 1;
			int count = 0, copy = n;
			while(copy % 2 == 0) {
				count++;
				copy /= 2;
			}
			boolean isPrime = n != 1;
			for(int i = 2; i * (long)i <= copy; i++) {
				if(copy % i == 0) {
					isPrime = false;
				}
			}
			String A = "Ashishgup", B = "FastestFinger";
			if(n == 1) {
				out.println(B);
			} else if(n == 2 || n % 2 == 1) {
				out.println(A);
			} else if(count > 1 && copy == 1) {
				out.println(B);
			} else {
				out.println((isPrime && count == 1) ? B : A);
			}
		}
		out.flush();
		out.close();
	}

}
