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 prime(int a) {
  int pu, po = 0;
  for (pu = 2; (pu * pu) <= a; pu++) {
    if (a % pu == 0) {
      po = 1;
      break;
    }
  }
  if (po == 0) {
    return 1;
  } else {
    return 0;
  }
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    long long n, i = 0, j = 0;
    cin >> n;
    if (((n > 1) && (n % 2)) || (n == 2)) {
      printf("Ashishgup\n");
    } else {
      long long c = 0, flag = 0;
      for (i = 2; (i * i) <= n; i++) {
        if (n % i == 0) {
          if (((i % 2) == 1) || (((n / i) % 2) == 1)) {
            c++;
            break;
          }
        }
      }
      if (c > 0) {
        if (n % 4 == 0) {
          flag = 1;
        } else if (prime(n / 2) == 1) {
          flag = 0;
        } else {
          flag = 1;
        }
      }
      if ((n == 1) || (c == 0) || (flag == 0)) {
        printf("FastestFinger\n");
      } else {
        printf("Ashishgup\n");
      }
    }
  }
  return 0;
}
