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.
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
bool primeFactors(long long n, long long* two, long long* factor) {
  while (n % 2 == 0) {
    (*two)++;
    n = n / 2;
  }
  bool flag = false;
  if (n > 1) {
    flag = true;
    (*factor)++;
  }
  for (int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      (*factor)++;
      flag = true;
      if ((*factor) > 1) {
        break;
      }
      n = n / i;
    }
    if (flag && (*factor) > 1) {
      break;
    }
  }
  return flag;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger" << '\n';
    } else if (n == 2) {
      cout << "Ashishgup" << '\n';
    } else {
      if (n % 2 == 1) {
        cout << "Ashishgup" << '\n';
      } else {
        long long two = 0, factor = 0;
        if (primeFactors(n, &two, &factor)) {
          if (factor == 1) {
            if (two == 1) {
              cout << "FastestFinger" << '\n';
            } else {
              cout << "Ashishgup" << '\n';
            }
          } else {
            cout << "Ashishgup" << '\n';
          }
        } else {
          cout << "FastestFinger" << '\n';
        }
      }
    }
  }
}
