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 vi = std::vector<int>;
using pii = std::pair<int, int>;
using vii = std::vector<pii>;
using ll = long long;
int solve();
int main(int argc, char* argv[]) {
  int t = 1;
  scanf("%d", &t);
  while (t--) {
    solve();
  }
}
bool play(const int n) {
  static std::map<int, bool> cache;
  if (n == 1) {
    return false;
  }
  if (n % 2 == 1) {
    return true;
  }
  auto it = cache.find(n);
  if (it != cache.end()) {
    return (*it).second;
  }
  if (!play(n - 1)) {
    cache[n] = true;
    return true;
  }
  for (int i = 2; i * i <= n; i++) {
    if (n % i != 0) continue;
    int d = n / i;
    if (i % 2 == 1 && !play(d)) {
      cache[n] = true;
      return true;
    }
    if (d % 2 == 1 && !play(i)) {
      cache[n] = true;
      return true;
    }
  }
  cache[n] = false;
  return false;
}
int solve() {
  int n;
  scanf("%d", &n);
  if (play(n)) {
    puts("Ashishgup");
  } else {
    puts("FastestFinger");
  }
  return 0;
}
