#include <bits/stdc++.h>
using namespace std;
bool ip(long long n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
long long oddf(long long n) {
  while (n % 2 == 0) {
    n = n / 2;
  }
  long long c = 0;
  for (long long i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      n = n / i;
      c++;
    }
  }
  if (n > 2) c++;
  return c;
}
int32_t main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n = 0;
    cin >> n;
    long long k = n;
    if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n % 2 == 0) {
      if (n == 2)
        cout << "Ashishgup" << endl;
      else {
        if (ip(n) == true)
          cout << "FastestFinger" << endl;
        else {
          long long c = 0;
          while (n % 2 == 0) {
            n = n / 2;
            c++;
          }
          if (c == 1) {
            long long n_of = oddf(k);
            if (n_of % 2 == 0)
              cout << "Ashishgup" << endl;
            else {
              if (n_of == 1)
                cout << "FastestFinger" << endl;
              else
                cout << "Ashishgup" << endl;
            }
          } else
            cout << "Ashishgup" << endl;
        }
      }
    } else {
      cout << "Ashishgup" << endl;
    }
  }
}

### 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;
bool ip(long long n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
long long oddf(long long n) {
  while (n % 2 == 0) {
    n = n / 2;
  }
  long long c = 0;
  for (long long i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      n = n / i;
      c++;
    }
  }
  if (n > 2) c++;
  return c;
}
int32_t main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n = 0;
    cin >> n;
    long long k = n;
    if (n == 1)
      cout << "FastestFinger" << endl;
    else if (n % 2 == 0) {
      if (n == 2)
        cout << "Ashishgup" << endl;
      else {
        if (ip(n) == true)
          cout << "FastestFinger" << endl;
        else {
          long long c = 0;
          while (n % 2 == 0) {
            n = n / 2;
            c++;
          }
          if (c == 1) {
            long long n_of = oddf(k);
            if (n_of % 2 == 0)
              cout << "Ashishgup" << endl;
            else {
              if (n_of == 1)
                cout << "FastestFinger" << endl;
              else
                cout << "Ashishgup" << endl;
            }
          } else
            cout << "Ashishgup" << endl;
        }
      }
    } else {
      cout << "Ashishgup" << endl;
    }
  }
}

```