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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class ProblemC {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static boolean isPrime(long n) {

        if (n == 2) {
            return true;
        } else if (n < 2) {
            return false;
        }

        if (n % 2 == 0) {
            return false;
        }

        for (int i = 3; i <= Math.sqrt(n); i+=2) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
    public static List<PowerPair> getPrimeFactors(int n) {
        List<PowerPair> result = new ArrayList<>();

        for (int i = 2; i <= Math.sqrt(n); i++) {
            PowerPair pair = new PowerPair(i, 0);
            while (n % i == 0) {
                pair.exp++;
                n /= i;
            }

            if (pair.exp > 0) {
                result.add(pair);
            }
        }

        if (n != 1) {
            result.add(new PowerPair(n, 1));
        }

        return result;
    }
    static class PowerPair {
        public int base;
        int exp;

        public PowerPair(int base, int exp) {
            this.base = base;
            this.exp = exp;
        }

        @Override
        public String toString() {
            return base + "^" + exp;
        }
    }



    private final static String PLAYER_1 = "Ashishgup";
    private final static String PLAYER_2 = "FastestFinger";

    public static void main(String[] args) {
        FastReader reader = new FastReader();

        int t = reader.nextInt();

        for (int i = 0; i < t; i++) {
            int n = reader.nextInt();

            List<PowerPair> primeFactors = getPrimeFactors(n);
            if (n == 2) {
                System.out.println(PLAYER_1);
            } else if (primeFactors.size() == 1 && primeFactors.get(0).base == 2 || n == 1) {
                System.out.println(PLAYER_2);
            } else if (n % 2 == 1) {
                System.out.println(PLAYER_1);
            } else if (n % 4 == 0) {
                System.out.println(PLAYER_1);
            } else {
                if (isPrime(n / 2)) {
                    System.out.println(PLAYER_2);
                } else {
                    System.out.println(PLAYER_1);
                }
            }
        }
    }
}










