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.Scanner;
 
public class ng {
 
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn=new Scanner(System.in);
		int t =scn.nextInt();
		StringBuilder sb=new StringBuilder();
		while(t-->0){
			int n=scn.nextInt();
			int n1=n;
			if(n==1){
			sb.append("FastestFinger"+'\n');
			continue;
			}
			if(n==2){
				sb.append("Ashishgup"+'\n');
				continue;
			}
			if(n%2==1){
				sb.append("Ashishgup"+'\n');
				continue;
			}
			boolean f=false;
			int count=0;
			while(n>0 && (n%2==0)){
				n/=2;
				count++;
			}
			//System.out.println(n);
			boolean ans= isprime(n);
				
			
			//System.out.println(n+"a"+n1);
			if(n>1 && (ans==false||count>1)){
				sb.append("Ashishgup"+'\n');
				
			}else{
				sb.append("FastestFinger"+'\n');
			}
			
			
		}
		System.out.println(sb);
 
	}
	
	public static boolean isprime(int n){
		for(int i=2;i*i<=n;i++){
			if(n%i==0){
				return false;
			}
		}
		return true;
	}
 
}