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;
vector<long long int> fac(long long int n) {
  long long int i;
  vector<long long int> ans;
  for (i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      if (n / i == i)
        ans.push_back(i);
      else {
        ans.push_back(n / i);
        ans.push_back(i);
      }
    }
  }
  sort(ans.begin(), ans.end());
  return ans;
}
void solve() {
  long long int n;
  cin >> n;
  long long int val = 1;
  long long int t = n;
  while (t % 2 == 0 && t > 0) {
    val *= 2;
    t /= 2;
  }
  if (n == 1)
    cout << "FastestFinger"
         << "\n";
  else if (n == 2)
    cout << "Ashishgup"
         << "\n";
  else if (val == n)
    cout << "FastestFinger"
         << "\n";
  else if (n % 2 == 1)
    cout << "Ashishgup"
         << "\n";
  else {
    if (val > 2)
      cout << "Ashishgup"
           << "\n";
    else {
      n /= 2;
      vector<long long int> factor = fac(n);
      if (factor.size() == 0)
        cout << "FastestFinger"
             << "\n";
      else
        cout << "Ashishgup"
             << "\n";
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) solve();
  return 0;
}
