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 ARRMAX = 100001;
const long long INTMAX = LLONG_MAX;
void solve() {
  long long n;
  cin >> n;
  long long ans = 0;
  if (n == 1)
    ans = 1;
  else if (n == 2)
    ans = 0;
  else if (n % 2 == 1)
    ans = 0;
  else {
    std::vector<long long> v(5, 0);
    long long oddcount = 0;
    long long evencount = 0;
    long long final = n;
    while (n % 2 == 0) {
      n /= 2;
      evencount++;
    }
    if (n == 1) {
      ans = 1;
    } else if (evencount > 1)
      ans = 0;
    else {
      ans = 1;
      for (long long i = 2; i < sqrt(n) + 1; ++i) {
        if (n % i == 0) ans = 0;
      }
    }
  }
  if (ans == 1)
    cout << "FastestFinger"
         << "\n";
  else
    cout << "Ashishgup"
         << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  cin >> t;
  while (t-- > 0) solve();
  return 0;
}
