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 long long M = 1e18 + 7;
const int N = 1e6 + 1;
const int base = 31;
template <typename T1, typename T2>
long long gcd(T1 a, T2 b) {
  return (b == 0 ? a : gcd(b, a % b));
}
template <typename T1, typename T2>
long long lcm(T1 a, T2 b) {
  return 1LL * a / gcd(a, b) * b;
}
long long qp(unsigned long long A, int B) {
  long long ans = 1;
  while (B) {
    if (B % 2) ans = ans * A % M;
    A = 1LL * A * A % M;
    B /= 2;
  }
  return ans;
}
string s;
long long res, a[N], c[N], mx, t = 1, n, m;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  c[0] = 1;
  for (int i = 1; i <= 30; i++) c[i] = c[i - 1] * 2;
  cin >> t;
  while (t--) {
    res = mx = 0;
    cin >> n;
    if (n == 1 || m % 2) {
      cout << "FastestFinger"
           << "\n";
      continue;
    }
    if (n == 2 || n % 2) {
      cout << "Ashishgup"
           << "\n";
      continue;
    }
    n /= 2;
    while (n % 2 == 0) {
      n /= 2;
      res = 1;
    }
    if (n == 1) res = 0;
    for (int i = 3; i <= int(sqrt(n)); i += 2) {
      if (n % i)
        continue;
      else
        res = 1;
    }
    if (res == 0)
      cout << "FastestFinger"
           << " ";
    else
      cout << "Ashishgup"
           << " ";
    cout << "\n";
  }
  return 0;
}
