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;
using ll = long long;
ll MOD = 1000000007;
ll mod = 998244353;
int inf = 1000001000;
ll INF = 1e18 + 5;
int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
  int t;
  cin >> t;
  for (int(_) = 0; (_) < (t); (_)++) {
    int n;
    cin >> n;
    if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n == 2)
      cout << "Ashishgup" << endl;
    else {
      if (n % 2)
        cout << "Ashishgup" << endl;
      else {
        int cnt = 0;
        while (n % 2 == 0) {
          n /= 2;
          cnt++;
        }
        if (n == 1) {
          cout << "FastestFinger" << endl;
        } else {
          if (cnt > 1)
            cout << "Ashishgup" << endl;
          else {
            int q = 0;
            for (ll i = 3; i * i <= n; i += 2) {
              if (n % i == 0) {
                cout << "Ashishgup" << endl;
                q++;
                break;
              }
            }
            if (q == 0) cout << "FastestFinger" << endl;
          }
        }
      }
    }
  }
}
