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;
void solve() {
  long long n;
  cin >> n;
  if (n == 1) {
    cout << "FastestFinger\n";
    return;
  }
  if (n == 2) {
    cout << "Ashishgup\n";
    return;
  }
  if (n % 2 == 1) {
    cout << "Ashishgup\n";
    return;
  }
  long long ok = -1;
  set<long long> s;
  for (long long i = 3; i * i <= n * 2; i += 2) {
    if (n % i == 0) {
      s.insert(i);
      ok = i;
    }
    if (n % (i - 1) == 0 && n / (i - 1) % 2 != 0) {
      s.insert(n / (i - 1));
      ok = n / (i - 1);
    }
  }
  if (s.size() == 0 || (n / ok == 2 && s.size() == 1)) {
    cout << "FastestFinger\n";
    return;
  }
  cout << "Ashishgup\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cout << fixed;
  cout.precision(30);
  long long t = 1;
  cin >> t;
  while (t--) solve();
}
