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;
void solve() {
  long long n;
  cin >> n;
  if (n == 1)
    printf("FastestFinger\n");
  else if (n == 2 || n % 2 == 1)
    printf("Ashishgup\n");
  else {
    int flag = 0;
    while (n % 2 == 0) {
      n /= 2;
      flag++;
    }
    if (n == 1)
      printf("FastestFinger\n");
    else {
      int s = 0;
      for (int i = 3; i <= sqrt(n); i += 2)
        while (n % i == 0) {
          n /= i;
          s++;
          if (s > 1) break;
        }
      if (flag == 1) {
        if (s == 0)
          printf("FastestFinger\n");
        else
          printf("Ashishgup\n");
      } else
        printf("Ashishgup\n");
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  int t;
  cin >> t;
  while (t--) solve();
}
