#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int T, n, i, flag = 0;
  cin >> T;
  while (T--) {
    cin >> n;
    flag = 0;
    if (n % 2 != 0 && n != 1)
      cout << "Ashishgup" << endl;
    else if (n == 2)
      cout << "Ashishgup" << endl;
    else if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n % 2 == 0 && n > 2) {
      long long int c = 0, k = 0;
      while (n % 2 == 0) {
        c++;
        n = n / 2;
      }
      for (i = 3; i <= sqrt(n); i = i + 2) {
        while (n % i == 0) {
          k++;
          n = n / i;
        }
      }
      if (n > 2) k++;
      if (c == 1 && k == 1)
        cout << "FastestFinger" << endl;
      else if (c == 1 && k > 1)
        cout << "Ashishgup" << endl;
      else if (c >= 2 && k >= 1)
        cout << "Ashishgup" << endl;
      else if (c > 0 && k == 0)
        cout << "FastestFinger" << endl;
    }
  }
}

### Prompt

Your task is to create a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int T, n, i, flag = 0;
  cin >> T;
  while (T--) {
    cin >> n;
    flag = 0;
    if (n % 2 != 0 && n != 1)
      cout << "Ashishgup" << endl;
    else if (n == 2)
      cout << "Ashishgup" << endl;
    else if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n % 2 == 0 && n > 2) {
      long long int c = 0, k = 0;
      while (n % 2 == 0) {
        c++;
        n = n / 2;
      }
      for (i = 3; i <= sqrt(n); i = i + 2) {
        while (n % i == 0) {
          k++;
          n = n / i;
        }
      }
      if (n > 2) k++;
      if (c == 1 && k == 1)
        cout << "FastestFinger" << endl;
      else if (c == 1 && k > 1)
        cout << "Ashishgup" << endl;
      else if (c >= 2 && k >= 1)
        cout << "Ashishgup" << endl;
      else if (c > 0 && k == 0)
        cout << "FastestFinger" << endl;
    }
  }
}

```