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 ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
const ll MOD = 1e9 + 7;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const ld EPS = 1e-10;
template <typename T>
bool chmax(T &x, const T &y) {
  return (x < y) ? (x = y, true) : false;
};
template <typename T>
bool chmin(T &x, const T &y) {
  return (x > y) ? (x = y, true) : false;
};
int main() {
  string a = "Ashishgup", b = "FastestFinger";
  int T;
  cin >> T;
  for (int t = 0; t < T; t++) {
    int N;
    cin >> N;
    if (N == 1) {
      cout << b << endl;
      continue;
    }
    if (N % 2 == 1 || N == 2) {
      cout << a << endl;
      continue;
    }
    int cnt = 0;
    while (N % 2 == 0) N /= 2, cnt++;
    if (N == 1) {
      cout << b << endl;
      continue;
    }
    if (cnt >= 2) {
      cout << a << endl;
      continue;
    }
    bool flag = false;
    for (int i = 2; i * i <= N; i++) {
      if (N % i == 0) flag = true;
    }
    if (flag)
      cout << a << endl;
    else
      cout << b << endl;
  }
}
