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.BigInteger;
import java.util.*;
public class Main {
	static Scanner sc=new Scanner(System.in);
	static int ans=0,n,m;
	static char a[][];
	public static void main(String[] args) {
		//show();
		for(int t=sc.nextInt();t>0;t--) {
			show();
		}
	}
	private static void show() {
		int n=sc.nextInt();
		if(n==1)System.out.println("FastestFinger");
		else if(n==2||n%2==1)System.out.println("Ashishgup");
		else {
			boolean bool=false;
			for(int i=2;i*i<=n;i++) {
				if(n%i!=0)	continue;
				if(i%2==1&&(n/i)!=2)	bool=true;//比如56/7
				if((n/i)%2==1&&i!=2)	bool=true;
			}
			if(!bool)System.out.println("FastestFinger");
			else System.out.println("Ashishgup");
		}
		
		
	}
}
