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;
using namespace std;
vector<pair<int, int> > Divisors(int n) {
  vector<pair<int, int> > v;
  int two = 0, odd = 0;
  while (n % 2 == 0) {
    two += 1;
    n = n / 2;
  }
  for (int i = 3; i <= sqrt(n); i += 2) {
    while (n % i == 0) {
      odd += 1;
      n = n / i;
    }
  }
  if (n > 2) odd++;
  v.push_back(make_pair(two, odd));
  return v;
}
int32_t main() {
  int i, j, n, coun, flag;
  int t;
  cin >> t;
  while (t--) {
    cin >> n;
    coun = 0;
    flag = 0;
    if (n == 1) {
      cout << "FastestFinger" << '\n';
      continue;
    }
    if (n % 2 != 0 && n > 1) {
      cout << "Ashishgup" << '\n';
      continue;
    }
    vector<pair<int, int> > fact;
    fact = Divisors(n);
    if (fact[0].first == 1 && fact[0].second == 0) cout << "Ashishgup" << '\n';
    if (fact[0].first > 1 && fact[0].second == 0)
      cout << "FastestFinger" << '\n';
    if (fact[0].second > 1) cout << "Ashishgup" << '\n';
    if (fact[0].first == 1 && fact[0].second == 1)
      cout << "FastestFinger" << '\n';
    if (fact[0].first > 1 && fact[0].second == 1) cout << "Ashishgup" << '\n';
  }
  return 0;
}
