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.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {
    static long mod = (long) 1e9 + 7;
    static long mod1 = 998244353;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);


        int t = in.nextInt();
        while (t-- > 0) {

            int n = in.nextInt();
            if (n % 2 == 1) {
                if (n != 1)
                    out.println("Ashishgup");
                else
                    out.println("FastestFinger");
            } else {
                ArrayList<Integer> ll = new ArrayList<>();
                primeFactors(n, ll);

                int even = 0;
                int odd = 0;
                for (int i : ll) {
                    if (i % 2 == 0)
                        even++;
                    else
                        odd++;
                }

                if (odd > 0) {
                    if (even == 1) {
                        if (odd > 1)
                            out.println("Ashishgup");
                        else
                            out.println("FastestFinger");
                    } else
                        out.println("Ashishgup");
                } else {
                    if (even == 1)
                        out.println("Ashishgup");
                    else
                        out.println("FastestFinger");
                }
            }

        }
        out.close();
    }

    public static void primeFactors(int n, ArrayList<Integer> ll) {
        while (n % 2 == 0) {
            ll.add(2);
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            while (n % i == 0) {
                ll.add(i);
                n /= i;
            }
        }
        if (n > 2)
            ll.add(n);
    }


    static final Random random = new Random();

    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static long gcd(long x, long y) {
        if (x == 0)
            return y;
        if (y == 0)
            return x;
        long r = 0, a, b;
        a = Math.max(x, y);
        b = Math.min(x, y);
        r = b;
        while (a % b != 0) {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }

    static long modulo(long a, long b, long c) {
        long x = 1, y = a % c;
        while (b > 0) {
            if (b % 2 == 1)
                x = (x * y) % c;
            y = (y * y) % c;
            b = b >> 1;
        }
        return x % c;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    static String printPrecision(double d) {
        DecimalFormat ft = new DecimalFormat("0.00000000000");
        return String.valueOf(ft.format(d));
    }

    static int countBit(long mask) {
        int ans = 0;
        while (mask != 0) {
            mask &= (mask - 1);
            ans++;
        }
        return ans;
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public int[] readArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = nextInt();
            return arr;
        }
    }
}