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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;

public class C {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        String p1 = "Ashishgup";
        String p2 = "FastestFinger";
        int t = Integer.parseInt(bf.readLine());
        for (int i = 0; i < t; i++) {
            long n = Long.parseLong(bf.readLine());
            if (n == 1) {
                out.println(p2);
            } else if (n == 2) {
                out.println(p1);
            } else if (n % 2 == 1) {
                out.println(p1);
            } else {
                // it's even
                // are there odd divisors to remove?
                if ((n & (n - 1)) == 0) { // power of 2
                    out.println(p2);
                } else {
                    // there are odd prime divisors
                    if (n % 4 == 0) {
                        // just remove all the prime divisors at once, we win
                        out.println(p1);
                    } else {
                        // there's only one 2, we win as long as there's
                        // at least 2 odd prime factors (remove k - 1)
                        if (isPrime(n / 2)) {
                            out.println(p2);
                        } else {
                            out.println(p1);
                        }
                    }
                }
            }
        }
        out.close();
        System.exit(0);
    }

    public static boolean isPrime(long n) {
        if (n > 100) {
            BigInteger bigint = new BigInteger(String.valueOf(n));
            return bigint.isProbablePrime(15);
        }
        long ub = ((long)Math.sqrt(n))+1;
        for (long i = 3; i < (n + 1)/2; i+=2) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}