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;
vector<int> primes;
vector<int> get_primes(int n) {
  vector<bool> is_prime(n + 1, true);
  for (int i = 2; i <= n; i++)
    if (is_prime[i])
      for (int j = i * i; j <= n; j += i) is_prime[j] = false;
  vector<int> primes;
  for (int i = 2; i <= n; i++)
    if (is_prime[i]) primes.push_back(i);
  return primes;
}
vector<int> get_factors(int n) {
  vector<int> factors;
  for (int i = 0; i < primes.size() && n > 1; i++) {
    int p = primes[i];
    while (n % p == 0) {
      factors.push_back(p);
      n /= p;
    }
  }
  if (n > 1) factors.push_back(n);
  return factors;
}
bool okay(int n) {
  if (n == 1) return false;
  if (n == 2) return true;
  if (n % 2 != 0) return true;
  auto factors = get_factors(n);
  int two_count = 0;
  int odd_count = 0;
  for (auto factor : factors)
    if (factor % 2 == 0)
      two_count++;
    else
      odd_count++;
  if (odd_count == 0) return false;
  if (two_count != 1) return true;
  return odd_count > 1;
}
int main() {
  int n, t;
  primes = get_primes(32000);
  cin >> t;
  while (t--) {
    cin >> n;
    cout << (okay(n) ? "Ashishgup" : "FastestFinger") << endl;
  }
  return 0;
}
