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 = (long long)(1e9 + 7);
const long long INF = (long long)(1e13 + 7);
const double EPS = 1e-14;
const double PI = acos(-1);
long long CEIL(long long a, long long b) {
  return (a >= 0 ? (a + (b - 1)) / b : (a - (b - 1)) / b);
}
long long mod(long long a, long long b) {
  return a >= 0 ? a % b : a - (b * CEIL(a, b));
}
long long bpm(long long a, long long b) {
  long long res = 1;
  for (a %= MOD; b; a = a * a % MOD, b >>= 1)
    if (b & 1) res = res * a % MOD;
  return res;
}
vector<long long> prime_list;
void prime_factorization(long long n) {
  while (n % 2 == 0) {
    n /= 2;
    prime_list.push_back(2);
  }
  for (long long i = 3; i < (long long)(sqrt((double)n)) + 2; i += 2)
    if (n % i == 0)
      while (n % i == 0) {
        n /= i;
        prime_list.push_back(i);
      }
  if (n != 1) prime_list.push_back(n);
}
class CNumberGame {
 public:
  static void solve(istream &cin, ostream &cout) {
    long long t;
    cin >> t;
    for (long long _ = 0; _ < (long long)(t); _++) {
      long long n;
      cin >> n;
      long long turn = 0;
      while (n != 1) {
        if (n % 2) {
          n = 1;
        } else if (n == 2) {
          n--;
        } else {
          prime_list = {};
          prime_factorization(n);
          long long odd = 0;
          long long even = 0;
          for (auto &i : prime_list) {
            if (i % 2) {
              odd++;
            } else {
              even++;
            }
          }
          if (odd == 0) {
            n -= 1;
          } else if (even == 1 and odd == 1) {
            n = 2;
          } else {
            n = 1;
          }
        }
        turn++;
      }
      if (turn % 2) {
        cout << "Ashishgup" << endl;
      } else {
        cout << "FastestFinger" << endl;
      }
    }
  }
};
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  CNumberGame solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return 0;
}
