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 mod = 1e9 + 7;
const double eps = 1e-8;
const int inf = 0x3f3f3f3f;
const int N = 2e5 + 10;
int vis[2010];
int a[N];
int main() {
  int n, m, q, k;
  cin >> q;
  while (q--) {
    cin >> n;
    if (n & 1 || n == 2) {
      if (n == 1)
        cout << "FastestFinger" << '\n';
      else
        cout << "Ashishgup" << '\n';
      continue;
    }
    vector<int> v;
    for (long long i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        if (i & 1) v.push_back(i);
        if (n / i != i && (n / i) % 2 == 1) v.push_back(n / i);
      }
    }
    if (v.size() == 0)
      cout << "FastestFinger";
    else {
      int f = 0;
      for (auto x : v) {
        if (n / x != 2) {
          f = 1;
          break;
        }
      }
      if (f)
        cout << "Ashishgup";
      else
        cout << "FastestFinger";
    }
    cout << '\n';
  }
}
