#include <bits/stdc++.h>
using namespace std;
int main() {
  long long t;
  cin >> t;
  while (t > 0) {
    long long n, m, k, ans;
    cin >> n;
    if (n == 1) {
      ans = 1;
    } else if (n == 2) {
      ans = 2;
    } else if (n > 2) {
      if (n % 2 == 0) {
        m = 0;
        while (n % 2 == 0) {
          n = n / 2;
          m++;
        }
        if (m == 1) {
          k = 3;
          long long fail = 1;
          while (k <= sqrt(n) && fail == 1) {
            if (n % k == 0) {
              fail = 0;
            }
            k = k + 2;
          }
          if (fail == 1) {
            ans = 1;
          } else {
            ans = 2;
          }
        } else {
          if (n == 1) {
            ans = 1;
          } else {
            ans = 2;
          }
        }
      } else {
        ans = 2;
      }
    }
    if (ans == 1) {
      cout << "FastestFinger" << endl;
    } else {
      cout << "Ashishgup" << endl;
    }
    t--;
  }
  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;
int main() {
  long long t;
  cin >> t;
  while (t > 0) {
    long long n, m, k, ans;
    cin >> n;
    if (n == 1) {
      ans = 1;
    } else if (n == 2) {
      ans = 2;
    } else if (n > 2) {
      if (n % 2 == 0) {
        m = 0;
        while (n % 2 == 0) {
          n = n / 2;
          m++;
        }
        if (m == 1) {
          k = 3;
          long long fail = 1;
          while (k <= sqrt(n) && fail == 1) {
            if (n % k == 0) {
              fail = 0;
            }
            k = k + 2;
          }
          if (fail == 1) {
            ans = 1;
          } else {
            ans = 2;
          }
        } else {
          if (n == 1) {
            ans = 1;
          } else {
            ans = 2;
          }
        }
      } else {
        ans = 2;
      }
    }
    if (ans == 1) {
      cout << "FastestFinger" << endl;
    } else {
      cout << "Ashishgup" << endl;
    }
    t--;
  }
  return 0;
}

```