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 int N = 1e5 + 5, INF = 1e9 + 7;
int main() {
  int q;
  cin >> q;
  while (q--) {
    int n;
    cin >> n;
    bool cur = 0;
    int me = INF;
    for (int i = 1; i * 1ll * i <= n; i++) {
      if (n % i) continue;
      if (n % i == 0 and i > 1 and i % 2) {
        cur = 1;
        me = min(me, i);
      }
      int j = i;
      i = n / i;
      if (n % i == 0 and i > 1 and i % 2) {
        cur = 1;
        me = min(me, i);
      }
      i = j;
    }
    if (me != INF) n /= me;
    if (n == 2) {
      cur ^= 1;
    }
    if (cur) {
      cout << "Ashishgup\n";
    } else {
      cout << "FastestFinger\n";
    }
  }
}
