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 ll = long long;
using ld = long double;
using namespace std;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
ll modlaber(ll a, ll m = 998244353) { return ((a + m) % m + m) % m; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int __;
  cin >> __;
  string a = "Ashishgup\n";
  string b = "FastestFinger\n";
  while (__--) {
    int n;
    cin >> n;
    if (n & 1 && n > 1 || n == 2) {
      cout << a;
      continue;
    }
    if (n == 1) {
      cout << b;
      continue;
    }
    int sana = 0;
    while (n % 2 == 0) sana++, n /= 2;
    if (n == 1)
      cout << b;
    else if (sana > 1)
      cout << a;
    else {
      bool ok = 0;
      for (int now = 2; now * now <= n; now++) ok |= n % now == 0;
      cout << (ok ? a : b);
    }
  }
  return 0;
}
