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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

/**
 * @project: Codeforces651
 * @author: izhanatuly
 * @date: 20/06/2020
 */
public class C {
    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int cases = scanner.nextInt();
        for (int t = 0; t < cases; t++) {
            runTestCase();
        }
    }

    public static void runTestCase() {
        long n = scanner.nextLong();
        if(n==1) {
            System.out.println("FastestFinger");
        } else if(n==2) {
            System.out.println("Ashishgup");
        } else if(n%2==1) {
            System.out.println("Ashishgup");
        } else {
            // count zeros
            int zeros = 0;
            for(long i=0; i<64; i++) {
                long mask = 1<<i;
                if((mask&n)==0) {
                    zeros++;
                } else {
                    break;
                }
            }
            long firstPart = n;
            while((firstPart&1)==0) {
                firstPart >>= 1;
            }
            // check power of 2
            if(firstPart == 1) {
                System.out.println("FastestFinger");
                return;
            }
            if(zeros > 1 || !isPrime(firstPart)) {
                System.out.println("Ashishgup");
            } else {
                System.out.println("FastestFinger");
            }
        }
    }

    private static boolean isPrime(long firstPart) {
        for(long i=2; i*i <= firstPart; i++) {
            if(firstPart%i == 0) return false;
        }
        return true;
    }
}
