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;
long long int power(long long int n) {
  long long int ans = 0;
  while (n % 2 == 0) {
    ans++;
    n /= 2;
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    string ans = "Ashishgup";
    if (n == 1)
      ans = "FastestFinger";
    else if (n & 1)
      ans = "Ashishgup";
    else if (n > 2) {
      long long int two = power(n);
      if ((1 << two) == n)
        ans = "FastestFinger";
      else if (two != 1)
        ans = "Ashishgup";
      else {
        ans = "FastestFinger";
        n /= (1 << two);
        long long int sq = sqrt(n);
        for (long long int i = 3; i <= sq; i += 2) {
          if (n % i == 0) {
            ans = "Ashishgup";
            break;
          }
        }
      }
    }
    cout << ans << endl;
  }
}
