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 c {

	public static void main(String[] args) {

		Scanner kb = new Scanner(System.in);
		int t = kb.nextInt();
		
		for(int cc=0; cc<t; cc++) {
			int n = kb.nextInt();
			
			if(n%2==1){
				if(n==1) {
					System.out.println("FastestFinger");
				}else {
					System.out.println("Ashishgup");
				}
			}else {
				int odd = 0;
				
				
				if(n%4==2) {
					
					odd = 1;
					
					for(int i=3; i<=Math.sqrt(n/2)&&odd<2; i+=2) {
						if(n%i==0) {
							odd++;
						}
					}
					
					if(odd>1) {
						System.out.println("Ashishgup");
					}else {
						if(n==2) {
							System.out.println("Ashishgup");
						}else {
							System.out.println("FastestFinger");
						}
					}
				}else {
					
					while(n%2==0) {
						n = n/2;
					}
					
					if(n>1) {
						System.out.println("Ashishgup");
					}else {
						System.out.println("FastestFinger");
					}
				}
				
			}

		}
	}

}