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;
using ll = long long;
using pii = pair<int, int>;
using pid = pair<int, double>;
using pdd = pair<double, double>;
using pic = pair<int, char>;
using pllll = pair<ll, ll>;
using pllc = pair<ll, char>;
using pill = pair<int, ll>;
using pss = pair<string, string>;
using pis = pair<int, string>;
using plls = pair<ll, string>;
using plld = pair<ll, double>;
using vi = vector<int>;
using vd = vector<double>;
using vc = vector<char>;
using vs = vector<string>;
int pfactors(int n, int pf[]) {
  int i = 0;
  while (n % 2 == 0) {
    pf[i] = 2;
    n /= 2;
    i++;
  }
  for (int j = 3; j <= sqrt(n); j += 2) {
    while (n % j == 0) {
      pf[i] = j;
      n /= j;
      i++;
    }
  }
  if (n > 2) {
    pf[i] = n;
    i++;
  }
  return i;
}
int main() {
  ios::sync_with_stdio(false);
  int t;
  cin >> t;
  int n;
  while (t--) {
    cin >> n;
    int pf[100005];
    int nopf = pfactors(n, pf);
    int two = 0;
    int odd = 0;
    for (int i = 0; i < nopf; i++) {
      if (pf[i] == 2) {
        two++;
      } else {
        odd++;
      }
    }
    if (n == 1) {
      cout << "FastestFinger"
           << "\n";
    } else if (n == 2) {
      cout << "Ashishgup"
           << "\n";
    } else if (odd == 0) {
      cout << "FastestFinger"
           << "\n";
    } else if (odd == nopf) {
      cout << "Ashishgup"
           << "\n";
    } else {
      if (two > 1) {
        cout << "Ashishgup"
             << "\n";
      } else {
        if (odd == 1) {
          cout << "FastestFinger"
               << "\n";
        } else {
          cout << "Ashishgup"
               << "\n";
        }
      }
    }
  }
  return 0;
}
