#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    bool win = false;
    if (n % 2 != 0 && n > 1) win = true;
    bool div_even = false;
    bool div_odd = false;
    if (n % 2 == 0) div_even = true;
    for (long long int i = 2; i * i <= n; i++) {
      if (n % i == 0 && i % 2 == 1) div_odd = true;
      long long int temp = n / i;
      if (temp % 2 != 0 && n % i == 0) div_odd = true;
    }
    if (div_odd == true) {
      if (n % 4 == 0)
        win = true;
      else if (div_even == true) {
        long long int m = n / 2;
        bool prime = true;
        for (long long int i = 2; i * i <= m; i++) {
          if (m % i == 0) prime = false;
        }
        if (prime == false) win = true;
      }
    }
    if (n == 1) win = false;
    if (n == 2) win = true;
    if (win == true)
      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;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    bool win = false;
    if (n % 2 != 0 && n > 1) win = true;
    bool div_even = false;
    bool div_odd = false;
    if (n % 2 == 0) div_even = true;
    for (long long int i = 2; i * i <= n; i++) {
      if (n % i == 0 && i % 2 == 1) div_odd = true;
      long long int temp = n / i;
      if (temp % 2 != 0 && n % i == 0) div_odd = true;
    }
    if (div_odd == true) {
      if (n % 4 == 0)
        win = true;
      else if (div_even == true) {
        long long int m = n / 2;
        bool prime = true;
        for (long long int i = 2; i * i <= m; i++) {
          if (m % i == 0) prime = false;
        }
        if (prime == false) win = true;
      }
    }
    if (n == 1) win = false;
    if (n == 2) win = true;
    if (win == true)
      cout << "Ashishgup" << endl;
    else
      cout << "FastestFinger" << endl;
  }
  return 0;
}

```