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.*;

/**
 * User :- sudhakar
 * Date :- 20/06/20
 * Time :- 8:15 PM
 */

public class NumberGame {
    private static final Reader r = new Reader();
    static final int MOD = 1000000007, SEIVE_SIZE = 10000000;
    static final int MAX = Integer.MAX_VALUE;
    static final int MIN = Integer.MIN_VALUE;
    static int[] spf;


    // CODE STARTS HERE
    public static void main(String[] args) throws IOException {
        int T = ni();
//        FastestFinger
//                Ashishgup
        while (T-- > 0) {
            int n = ni();
            String res = null;
            if (n == 1)
                res = "FastestFinger";
            else if (n == 2)
                res = "Ashishgup";
            else if ((n & 1) == 1)
                res = "Ashishgup";
            else if (isPowerOfTwo(n)) {
                res = "FastestFinger";
            } else {
                if (isPrime(n / 2)) res = "FastestFinger";
                else res = "Ashishgup";
            }
            System.out.println(res);
        }
    }
    // SOLUTION ENDS HERE


    /*Inner class for fast input*/
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String nextString() throws IOException {
            byte c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            StringBuilder builder = new StringBuilder();
            builder.append((char) c);
            c = read();
            while (!Character.isWhitespace(c)) {
                builder.append((char) c);
                c = read();
            }
            return builder.toString();
        }

        public char nextChar() throws IOException {
            byte c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            return (char) c;
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        public int[] nextIntArray(Reader r, int size) throws IOException {
            int[] arr = new int[size + 1];
            for (int i = 1; i <= size; i++)
                arr[i] = r.nextInt();
            return arr;
        }

        public long[] nextLongArray(Reader r, int size) throws IOException {
            long[] arr = new long[size + 1];
            for (int i = 1; i <= size; i++)
                arr[i] = r.nextLong();
            return arr;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    private static int ni() throws IOException {
        return r.nextInt();
    }

    private static long nl() throws IOException {
        return r.nextLong();
    }

    private static char nc() throws IOException {
        return r.nextChar();
    }

    private static double nd() throws IOException {
        return r.nextDouble();
    }

    private static String ns() throws IOException {
        return r.nextString();
    }

    private static int[] nextIntArr(int size) throws IOException {
        return r.nextIntArray(r, size);
    }

    private static long[] nextLongArr(int size) throws IOException {
        return r.nextLongArray(r, size);
    }

    private static boolean isPrime(int n) {
        for (int i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }

    private static boolean isPowerOfTwo(long c) {
        return (c & (c - 1)) == 0;
    }

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

    static void sieve() {
        spf = new int[SEIVE_SIZE + 1];
        spf[1] = 1;
        for (int i = 1; i <= SEIVE_SIZE; i += 2)
            spf[i] = i;
        for (int i = 2; i <= SEIVE_SIZE; i += 2)
            spf[i] = 2;
        for (int i = 3; i * i <= SEIVE_SIZE; i++) {
            // checking if i is prime 
            if (spf[i] == i) {
                // marking SPF for all numbers divisible by i 
                for (int j = i * i; j < SEIVE_SIZE; j += i)
                    // marking spf[j] if it is not  
                    // previously marked 
                    if (spf[j] == j)
                        spf[j] = i;
            }
        }
    }
}
