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 C { // WA 2

    public static void main(String[] args) {
        try {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
            int testCnt = Integer.parseInt(br.readLine());
            for (int i = 0; i < testCnt; i++) {
                int n = Integer.parseInt(br.readLine());
                int oneCnt = 0;
                int j = n;
                while (n > 0) {
                    if ((n & 1) == 1) oneCnt++;
                    n >>= 1;
                }
                if (j == 1) bw.write("FastestFinger\n");
                else if (j == 2) bw.write("Ashishgup\n");
                else if ((j & 1) == 1) bw.write("Ashishgup\n");
                else if (oneCnt == 1) bw.write("FastestFinger\n");
                else {
                    j /= 2;
                    if ((j & 1) == 1) {
                        int beforeDiv = j;
                        for (int k = 3; k <= Math.sqrt(j); k += 2) {
                            if (j % k == 0) {
                                j /= k;
                                break;
                            }
                        }
                        if (j == beforeDiv) bw.write("FastestFinger\n");
                        else bw.write("Ashishgup\n");
                    }
                    else bw.write("Ashishgup\n");
                }
            }
            br.close();
            bw.close();
        }
        catch (Exception e) {
            e.printStackTrace();
        }
    }

    public static void dbug(String s, long ... a) { // /*
        String[] line = s.split("<>");
        for (int i = 0; i < a.length; i++) {
            System.out.print(line[i] + a[i]);
        }
        System.out.println(line[a.length]); // */
    }

    public static void print(int[] a) { // /*
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
        System.out.println(); // */
    }
}