#include <bits/stdc++.h>
using namespace std;
using ll = long long int;
bool isPrime(int n) {
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) return false;
  }
  return true;
}
int f(int n) {
  if (n == 1) return 0;
  if (n == 2) return 1;
  if (n % 2) return 1;
  if (n % 4) return !isPrime(n / 2);
  while (n % 2 == 0) n /= 2;
  return n == 1 ? 0 : 1;
}
void solve(int n) {
  if (f(n)) {
    cout << "Ashishgup\n";
  } else {
    cout << "FastestFinger\n";
  }
}
int main() {
  int t;
  cin >> t;
  for (int i = 0; i < t; ++i) {
    int n;
    cin >> n;
    solve(n);
  }
  return 0;
}

### Prompt

Create a solution in CPP for 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;
using ll = long long int;
bool isPrime(int n) {
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) return false;
  }
  return true;
}
int f(int n) {
  if (n == 1) return 0;
  if (n == 2) return 1;
  if (n % 2) return 1;
  if (n % 4) return !isPrime(n / 2);
  while (n % 2 == 0) n /= 2;
  return n == 1 ? 0 : 1;
}
void solve(int n) {
  if (f(n)) {
    cout << "Ashishgup\n";
  } else {
    cout << "FastestFinger\n";
  }
}
int main() {
  int t;
  cin >> t;
  for (int i = 0; i < t; ++i) {
    int n;
    cin >> n;
    solve(n);
  }
  return 0;
}

```