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 Divisors(long long n) {
  vector<long long> v;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i) {
        v.push_back(i);
      } else {
        v.push_back(i);
        v.push_back(n / i);
      }
    }
  }
  int c = 0, i;
  for (i = 0; i < v.size(); i++) {
    if (v[i] % 2 == 1 && v[i] != (n / 2) && v[i] != 1) {
      return 1;
    }
  }
  return 2;
}
long long power(long long base, long long pow, long long mo) {
  long long res = 1;
  while (pow) {
    if (pow & 1) res = (res * base) % mo;
    base = (base * base) % mo;
    pow /= 2;
  }
  return res;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t, n, i, j, k, mini, l1, l2, l3, r1, r2, c, d, maxi, x, y, l, m, r,
      ans, last, flag, lastind;
  t = 1;
  cin >> t;
  while (t--) {
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger"
           << "\n";
    } else if (n % 2 == 1) {
      cout << "Ashishgup"
           << "\n";
    } else if (n == 2) {
      cout << "Ashishgup"
           << "\n";
    } else {
      x = Divisors(n);
      if (x == 1) {
        cout << "Ashishgup"
             << "\n";
      } else {
        cout << "FastestFinger"
             << "\n";
      }
    }
  }
}
