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.math.*;
import java.util.*;
public class R651Q3 {

	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();
			String A = "Ashishgup";
			String F = "FastestFinger";
			String ans = "";
			if (N%2==1&&N>1) ans="Ashishgup";
			else if (N==1) ans="FastestFinger";
			else {
				int num2 = 0;
				int numOdd = 0;
				while (N%2==0) {
					N/=2;
					num2++;
				}
				for (int p = 3; p*p<=N; p++) {
					int num = 0;
					while (N%p==0) {
						num++;
						N/=p;
					}
					if (num>0) numOdd+=num; //2 5s still do the job
				}
				if (N>1) numOdd++;
				if (num2>=2&&numOdd>=1) ans="Ashishgup";
				else if (num2==1&&numOdd>=2) ans=A;
				else if (num2==1&&numOdd==1) ans=F;
				else if (num2>=2) ans=F;
				else if (num2==1) ans=A;
			}
			System.out.println(ans);
		}
	}
}