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>
#pragma warning(disable : 4996)
using namespace std;
template <typename T>
void print(vector<T>& a) {
  for (int i = 0; i < a.size(); i++) cout << a[i] << ' ';
  cout << "\n";
}
template <typename T>
void print(deque<T>& a) {
  for (int i = 0; i < a.size(); i++) cout << a[i] << ' ';
  cout << "\n";
}
template <typename T>
void print(vector<vector<T>>& a) {
  for (int i = 0; i < a.size(); i++) {
    for (int j = 0; j < a[i].size(); j++) cout << a[i][j];
    cout << "\n";
  }
}
template <typename T>
void input(vector<T>& a) {
  for (int i = 0; i < a.size(); i++) cin >> a[i];
}
template <typename T>
void input(deque<T>& a) {
  for (int i = 0; i < a.size(); i++) cin >> a[i];
}
template <typename T>
void input(vector<vector<T>>& a) {
  for (int i = 0; i < a.size(); i++)
    for (int j = 0; j < a[i].size(); j++) cin >> a[i][j];
}
const int INF = 1e8;
const long long MOD = 998244353;
const int NMAX = 1e4 + 5;
double eps = 1e-8;
int n;
vector<vector<int>> g;
vector<bool> used;
vector<int> color;
vector<int> time_in, time_out;
int dfs_timer = 0;
bool is_prime(int x) {
  for (int i = 2; i <= sqrt(x); i++) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
void solve() {
  long long n;
  cin >> n;
  if ((n % 2 != 0 && n > 1) || n == 2)
    cout << "Ashishgup"
         << "\n";
  else {
    long long n1 = 2;
    while (n1 < n) {
      n1 *= 2;
    }
    if (n1 == n || n == 1)
      cout << "FastestFinger"
           << "\n";
    else {
      long long n1 = n;
      long long count = 0;
      while (n1 % 2 == 0) {
        n1 /= 2;
        count++;
      }
      if (n % 2 == 0 && is_prime(n / 2))
        cout << "FastestFinger"
             << "\n";
      else
        cout << "Ashishgup"
             << "\n";
    }
  }
}
int main() {
  srand(time(0));
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cout.setf(ios::fixed);
  cout.precision(10);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}
