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 q;
  cin >> q;
  while (q != 0) {
    int n;
    cin >> n;
    int one = 0;
    if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n == 2)
      cout << "Ashishgup" << endl;
    else if (n % 2 != 0)
      cout << "Ashishgup" << endl;
    else {
      int t = n;
      int count = 0, last = n;
      set<int> s;
      while (n != 1) {
        for (int i = 2; i <= sqrt(n); i++) {
          if ((n % i) == 0) {
            if (i % 2 != 0) {
              s.insert(i);
              count++;
            }
            n = (n / i);
          }
        }
        if (n == last) break;
        last = n;
      }
      if (n % 2 != 0) {
        s.insert(n);
        count++;
      }
      for (auto a : s) {
        t = (t / a);
      }
      if ((t == 2 && count != 1) || t == 1)
        cout << "Ashishgup" << endl;
      else if (t == 2 && count == 1)
        cout << "FastestFinger" << endl;
      else if (count != 0)
        cout << "Ashishgup" << endl;
      else
        cout << "FastestFinger" << endl;
    }
    q--;
  }
  return 0;
}
