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 MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long LL_INF = 0x3f3f3f3f3f3f3f3f;
const long double PI = acosl(-1.0l);
const long long MAXN = numeric_limits<long long>::max();
const long long MINN = (1e9 + 1);
void solve() {
  long long no;
  cin >> no;
  long long n = no;
  long long c = 0;
  if (n == 1) {
    cout << "FastestFinger\n";
    return;
  }
  if (n == 2) {
    cout << "Ashishgup\n";
    return;
  }
  vector<int> co;
  for (int i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      n /= i;
      if (i % 2 == 1) co.push_back(i);
    }
  }
  if (n > 1 && n % 2 == 1) co.push_back(n);
  if (co.size() == 0)
    cout << "FastestFinger\n";
  else if (co.size() == 1 && co[0] * 2 == no)
    cout << "FastestFinger\n";
  else
    cout << "Ashishgup\n";
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  srand(time(NULL));
  int t = 1;
  cin >> t;
  while (t) {
    t--;
    solve();
  }
  cerr << "time taken : " << (float)clock() / CLOCKS_PER_SEC << " secs" << endl;
  return 0;
}
