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.*;

final public class C {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder();
        int tst = Integer.parseInt(br.readLine());
        while(tst-->0){
            int n = Integer.parseInt(br.readLine());
            if(n%2 == 1){
                if(n == 1) sb.append("FastestFinger").append('\n');
                else sb.append("Ashishgup").append('\n');
            }
            else{
                if((n&(n-1)) == 0){
                    if(n == 2) sb.append("Ashishgup").append('\n');
                    else sb.append("FastestFinger").append('\n');
                }
                else{
                    if((n/2)%2 == 1){
                        int odd = n/2;
                        int divisors = 2;
                        for(int i = 2; i<=Math.sqrt(odd); i++){
                            if(divisors>2) break;
                            if(i*i == odd) divisors++;
                            int a = odd/i;
                            if(a*i == odd){
                                divisors+=2;
                            }
                        }
                        if(divisors>2) sb.append("Ashishgup").append('\n');
                        else sb.append("FastestFinger").append('\n');
                    }
                    else sb.append("Ashishgup").append('\n');
                }
            }
        }
        System.out.println(sb);
    }
}
