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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class CF {

	private static long[][][] dp;

	private static int res;
	private static boolean[][] vis;

	public static void main(String args[]) {
		Scanner input = new Scanner(System.in);
		int T = input.nextInt();
		for (int i = 1; i <= T; i++) {
			int n = input.nextInt();
			if (n == 1) {
				System.out.println("FastestFinger");
				continue;
			}
			if (n % 2 == 1 || n == 2) {
				System.out.println("Ashishgup");
				continue;
			}
			int pom = n;
			int pom2 = 1;
			while (pom % 2 == 0) {
				pom2 = pom2 * 2;
				pom = pom / 2;
			}
			n = n / pom2;
			int nn = n;
			int count = 0;
			for (int ii = 3; ii * ii  <= nn; ii = ii + 2) {
				while (n % ii == 0) {
					n = n / ii;
					count++;
				}
			}
			if (n != 1) {
				count++;
			}
			if (pom2 > 2) {
				count++;
			}
			if (count > 1) {
				System.out.println("Ashishgup");
			} else {
				System.out.println("FastestFinger");
			}
		}
	}

}