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;
int main() {
  long long int t, n, a, b;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    long long int rem = -1;
    long long int flag = 0;
    cin >> n;
    if (n % 2 != 0) {
      if (n == 1)
        cout << "FastestFinger" << endl;
      else
        cout << "Ashishgup" << endl;
    } else {
      if (n == 2) {
        cout << "Ashishgup" << endl;
      } else {
        vector<long long int> od_devisor;
        for (long long int i = 2; i * i <= n; i++) {
          if (n % i == 0) {
            if ((n % i) == i && (i % 2 != 0)) {
              od_devisor.push_back(i);
            } else {
              if (i % 2 != 0) od_devisor.push_back(i);
              if ((n / i) % 2 != 0) od_devisor.push_back(n / i);
            }
          }
        }
        for (long long int j = 0; j < od_devisor.size(); j++) {
          rem = n / od_devisor[j];
          if (rem != 2) {
            flag = 1;
          }
        }
        if (flag == 0) {
          cout << "FastestFinger" << endl;
        } else {
          cout << "Ashishgup" << endl;
        }
      }
    }
  }
  return 0;
}
