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.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        Scanner in = new Main().new Scanner(inputStream);
        Main solver = new Main();
        solver.runn(in);
    }

    long MOD = 1000000007L;

    public void runn(Scanner in) {
        int t = in.ni();
        while (t-- > 0) {
            int n = in.ni();
            boolean ashish = process(n);
            if (ashish)
                System.out.println("Ashishgup");
            else
                System.out.println("FastestFinger");
        }
    }

    int[] dp;

    public boolean process(int n) {
        if (n == 1) {
            return false;
        } else if (n % 2 == 1) {
            return true;
        } else {
            for (int i = 2; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    boolean owin = false;
                    if (i % 2 == 1) {
                        owin |= process(n / i);
                        if (!owin)
                            return true;
                    }
                    if ((n / i) % 2 == 1) {
                        owin |= process(i);
                        if (!owin)
                            return true;
                    }
                }
            }
            return !process(n - 1);
        }
    }

    class Scanner {
        BufferedReader br;
        StringTokenizer in;

        public Scanner(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            return hasMoreTokens() ? in.nextToken() : null;
        }

        public String rl() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                return null;
            }
        }

        boolean hasMoreTokens() {
            while (in == null || !in.hasMoreTokens()) {
                String s = rl();
                if (s == null)
                    return false;
                in = new StringTokenizer(s);
            }
            return true;
        }

        public String nextString() {
            return next();
        }

        public int ni() {
            return Integer.parseInt(nextString());
        }

        public double nd() {
            return Double.parseDouble(nextString());
        }

        public long nl() {
            return Long.parseLong(nextString());
        }

        public int[] nia(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] nla(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

    }

    int stoi(String a) {
        return Integer.parseInt(a);
    }

    void debug(int[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(long[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++)
                System.out.print(arr[i][j] + "\t");
            System.out.println();
        }
    }

    class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        public int compareTo(Pair other) {
            if (a == other.a)
                return Integer.compare(b, other.b);
            else
                return Integer.compare(a, other.a);
        }

        public int hashCode() {
            return a * 100007 + b;
        }

        public boolean equals(Object other) {
            Pair o = (Pair) other;
            return a == o.a && b == o.b;
        }
    }
}
