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;
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...);
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long int INF = (long long int)(1e18) + 7;
template <class T>
vector<pair<T, int>> factor(T x) {
  vector<pair<T, int>> pri;
  for (T i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      int t = 0;
      while (x % i == 0) x /= i, t++;
      pri.push_back({i, t});
    }
  if (x > 1) pri.push_back({x, 1});
  return pri;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n, m, t, i, j, k, ans = 0;
  cin >> t;
  while (t--) {
    cin >> n;
    ans = -1;
    if (n == 1) {
      ans = 1;
    } else if (n == 2) {
      ans = 0;
    } else if (n % 2) {
      ans = 0;
    } else {
      long long int pow2 = 0;
      while (n % 2 == 0) {
        n /= 2;
        pow2++;
      }
      if (pow2 > 1 and n > 1)
        ans = 0;
      else {
        auto fact = factor(n);
        if (fact.size() > 1)
          ans = 0;
        else if (fact.size() == 1 and fact[0].second > 1) {
          ans = 0;
        } else
          ans = 1;
      }
    }
    if (ans == 0)
      cout << "Ashishgup"
           << "\n";
    else
      cout << "FastestFinger"
           << "\n";
  }
  return 0;
}
