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.*;
import java.io.*;
 
public class Solution{
	static PrintWriter out=new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] input=br.readLine().trim().split(" ");
		int numTestCases=Integer.parseInt(input[0]);
		while(numTestCases-->0) {
			input=br.readLine().trim().split(" ");
			int n=Integer.parseInt(input[0]);
			out.println(getWinner(n));
		}
		out.flush();
		out.close();
	}		
	public static String getWinner(int n)
	{
		if(n==1) {
			return "FastestFinger";
		}
		if(n==2) {
			return "Ashishgup";
		}
		if(n%2!=0) {
			return "Ashishgup";
		}
		int temp=n;
		int num2s=0;
		while(n%2==0) {
			num2s++;
			n/=2;
		}
		int numOddFactors=0;
		for(int i=3;i<=Math.sqrt(n);i++) {
			while(n%i==0) {
				numOddFactors++;
				n/=i;
			}
		}
		
		if(n>1) {
			numOddFactors++;
		}
		
		if((temp&(temp-1))==0) {
			return "FastestFinger";
		}
		if(num2s>1 || numOddFactors>1){
			return "Ashishgup";
		}
		else {
			return "FastestFinger";
		}
	}
}