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.
#include <bits/stdc++.h>
using namespace std;
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  std::cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    if (n == 1) {
      std::cout << "FastestFinger\n";
    } else if (n % 2 == 1) {
      std::cout << "Ashishgup\n";
    } else {
      if (n % 4 == 0) {
        if (__builtin_popcount(n) > 1) {
          std::cout << "Ashishgup\n";
        } else {
          std::cout << "FastestFinger\n";
        }
      } else {
        int x = 0;
        for (int i = 2; i * i <= n; ++i) {
          if (n % i) continue;
          while (n % i == 0) {
            ++x;
            n /= i;
          }
        }
        if (n > 1) ++x;
        if (x ^ 2)
          std::cout << "Ashishgup\n";
        else
          std::cout << "FastestFinger\n";
      }
    }
  }
}
