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.util.*;

public class CfA {

    static class Reader {
        BufferedReader br;
        StringTokenizer st;

        public Reader() {
            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;
        }
    }

    static long binpow(int a, int b) {
        if (b == 0)
            return 1;
        long res = binpow(a, b / 2);
        if (b % 2 == 1)
            return res * res * a;
        else
            return res * res;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static long n, m, x, y, k;
    static long ans;
    static final int MAX_K = 10000000;
    static int[] spf = new int[MAX_K + 1];
    static List<Integer> freq;
    static int count2;

    public static long primeFactors() {
        count2 = 0;
        long toRet = 0;
        long new_n = 1;

        while (n % 2 == 0) {
            // System.out.print(2 + " ");
            n /= 2;
            new_n *= 2;
            count2++;
        }

        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i != 0)
                continue;
            int cnt = 0;
            while (n % i == 0) {
                // System.out.print(i + " ");
                n /= i;
                cnt++;
            }

            toRet += cnt;
        }

        if (n > 2) {
            // System.out.print(n);
            toRet += 1;
        }

        n = new_n;
        // System.out.println("\tnew n = " + n + " xor = " + toRet);
        return toRet;
    }

    public static void main(String[] args) throws Exception {
        Reader in = new Reader();
        int T = in.nextInt();
        while (T-- > 0) {
            n = in.nextInt();
            if (n == 2) {
                System.out.println("Ashishgup");
                continue;
            }

            if (n == 1) {
                System.out.println("FastestFinger");
                continue;
            }

            long num_odd_factors = primeFactors();
            if (count2 == 0)
                System.out.println("Ashishgup");
            else if (count2 == 1) {
                if (num_odd_factors > 1)
                    System.out.println("Ashishgup");
                else
                    System.out.println("FastestFinger");

            } else if (count2 > 1)
            {
                if(num_odd_factors >= 1)
                    System.out.println("Ashishgup");
                else
                    System.out.println("FastestFinger");
            }
                

        }
    }

}

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