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 int imax = INT32_MAX;
const int imin = INT32_MIN;
const long long int inf = 1e18;
const long long int MOD = 998244353;
const long long int range = 250;
template <class T>
T mx(T begin, T end) {
  return max_element(begin, end);
}
template <class T>
T mn(T begin, T end) {
  return min_element(begin, end);
}
template <class T>
void print(vector<T> nums) {
  for (T i : nums) cout << i << " ";
  cout << "\n";
}
template <class T>
void read(vector<T>& nums) {
  for (T& i : nums) cin >> i;
}
template <class T>
void alloc(vector<vector<T>*> nums, T n) {
  for (auto v : nums) v->resize(n + 1);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t = 1;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger\n";
      continue;
    }
    if (n == 2) {
      cout << "Ashishgup\n";
      continue;
    }
    if (n & 1) {
      cout << "Ashishgup";
    } else {
      if (!(n & (n - 1))) {
        cout << "FastestFinger";
      } else if ((n / 2) % 2 == 0) {
        cout << "Ashishgup";
      } else {
        int b = 0, temp = n;
        for (int i = 2; i * i <= n; ++i) {
          if (temp % i == 0) {
            int cnt = 0;
            while (temp % i == 0) {
              temp /= i;
              cnt++;
            }
            if (i & 1) {
              b += cnt;
            }
          }
        }
        if (temp > 1) b++;
        if (b > 1) {
          cout << "Ashishgup";
        } else {
          cout << "FastestFinger";
        }
      }
    }
    cout << "\n";
  }
  return 0;
}
