#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
bool prime(int n) {
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) return false;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long test_case;
  cin >> test_case;
  while (test_case--) {
    long long n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger" << endl;
    } else if (n % 2 == 1) {
      cout << "Ashishgup" << endl;
    } else {
      int d = n;
      int p = 0;
      while (d > 0 && d % 2 == 0) {
        p++;
        d /= 2;
      }
      int y = pow(2, p);
      if (y < n && p > 1) {
        cout << "Ashishgup" << endl;
      } else if (y < n && p == 1) {
        if (prime(n / 2))
          cout << "FastestFinger" << endl;
        else {
          cout << "Ashishgup" << endl;
        }
      } else {
        if (n == 2) {
          cout << "Ashishgup" << endl;
        } else
          cout << "FastestFinger" << endl;
      }
    }
  }
  return 0;
}

### Prompt

Please formulate 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;
const int MOD = 1e9 + 7;
bool prime(int n) {
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) return false;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long test_case;
  cin >> test_case;
  while (test_case--) {
    long long n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger" << endl;
    } else if (n % 2 == 1) {
      cout << "Ashishgup" << endl;
    } else {
      int d = n;
      int p = 0;
      while (d > 0 && d % 2 == 0) {
        p++;
        d /= 2;
      }
      int y = pow(2, p);
      if (y < n && p > 1) {
        cout << "Ashishgup" << endl;
      } else if (y < n && p == 1) {
        if (prime(n / 2))
          cout << "FastestFinger" << endl;
        else {
          cout << "Ashishgup" << endl;
        }
      } else {
        if (n == 2) {
          cout << "Ashishgup" << endl;
        } else
          cout << "FastestFinger" << endl;
      }
    }
  }
  return 0;
}

```