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 NumberGame {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int C = sc.nextInt();
        for (int i=0;i<C;i++) {
            FindWinner(sc);
        }
    }
    private static void FindWinner(Scanner sc){
        int n = sc.nextInt();
        if (n==1){
            System.out.println("FastestFinger");

        }else if (n%2==1||n==2 ) {
            System.out.println("Ashishgup");

        }else {
            if ((n/2)%2==1){
                if (!checkP(n/2)){
                    System.out.println("Ashishgup");
                }else {
                    System.out.println("FastestFinger");
                }
            }else if ((Math.log10(n)/Math.log10(2))%1==0){
                System.out.println("FastestFinger");
            }else {
                System.out.println("Ashishgup");
            }
        }
    }
    private static boolean checkP (int n){
        boolean isP = true;
        for (int i =2;i<Math.ceil(Math.sqrt(n))+1;i++){
            if ((n/i)*i==n){
                isP=false;
            }
        }
        return isP;
    }
}

/*
*  1.奇数 -> "Ashishgup"
*  2.偶数 -> 没有奇数因子 ->             "FastestFinger"
 *  3.偶数 -> 有奇数因子
*         Ashishgup  除以奇数因子
*          -> 偶数（没有奇数因子) ->(1. =2 2. >2)
*                   1.=2 FastestFinger
*                   2. >2 Ashishgup
*
*  18 / 3
*
*
* */