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;
const long long INF = 1000000007;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  cin >> t;
  string a = "Ashishgup";
  string f = "FastestFinger";
  while (t--) {
    int n;
    cin >> n;
    if (n == 1)
      cout << f << "\n";
    else if (n == 2)
      cout << a << "\n";
    else if (n % 2 == 0) {
      int z = n;
      while (z % 2 == 0) {
        z /= 2;
      }
      if (z != 1) {
        if (n % 4 == 0)
          cout << a << "\n";
        else {
          int ok = 0;
          for (int i = 3; i * i <= z; i++) {
            if (z % i == 0 && z / i > 1) {
              ok = 1;
              break;
            }
          }
          if (ok)
            cout << a << "\n";
          else
            cout << f << "\n";
        }
      } else {
        cout << f << "\n";
      }
    } else {
      cout << a << "\n";
    }
  }
  return 0;
}
