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.*;
import java.math.BigInteger;
import java.util.*;

/**
 * @author Tran Anh Tai
 * @template for CP codes
 */
public class ProbA {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        static int MOD = 998244353;
        public void solve(InputReader in, PrintWriter out) {
            int t = in.nextInt();
            for (int i = 0; i <  t; i++){
                int n = in.nextInt();
                if (n == 1){
                    out.println("FastestFinger");
                }
                else if (n == 2){
                    out.println("Ashishgup");
                }
                else if (n % 2 == 1){
                    out.println("Ashishgup");
                }
                else{
                    int cnt = 0;
                    while (n % 2 == 0){
                        n = n / 2;
                        cnt++;
                    }
                    if (cnt > 1){
                        if (n == 1){
                            out.println("FastestFinger");
                        }
                        else {
                            out.println("Ashishgup");
                        }
                    }
                    else{
                        if (isPrime(n)){
                            out.println("FastestFinger");
                        }
                        else{
                            out.println("Ashishgup");
                        }
                    }
                }
            }
        }
        public  boolean isPrime(int n){
            int d = (int)(Math.sqrt(n));
            for (int i = 2; i <= d; i++){
                if (n % i == 0){
                    return false;
                }
            }
            return true;
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}