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;
typedef long long ll;
template <typename tn>
inline tn next(void);
template <typename tn>
inline ostream& operator<<(ostream& os, const vector<tn>& v);
inline bool isPrime(ll e) {
  if (e <= 1) return 0;
  for (register ll i = 2; i <= sqrt(e) + 0.5; i++)
    if (!(e % i)) return 0;
  return 1;
}
vector<ll> prime;
signed Solving(void) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ll T = next<ll>();
  for (register ll i = 3; i <= 1e5; i++)
    if (isPrime(i)) prime.push_back(i);
  while (T--) {
    ll n = next<ll>(), cnt = 0, t = n, tot = 0;
    for (register ll i = 0; i < prime.size(); i++)
      while (!(t % prime[i])) cnt++, t /= prime[i];
    while (t % 2 == 0) t /= 2, tot++;
    if (isPrime(t)) cnt++;
    ;
    if (n == 1)
      cout << "FastestFinger" << '\n';
    else if (n == 2 || tot == 0)
      cout << "Ashishgup" << '\n';
    else if (cnt == 0 || (tot == 1 && cnt <= 1))
      cout << "FastestFinger" << '\n';
    else
      cout << "Ashishgup" << '\n';
  }
  return 0;
}
template <typename tn>
inline tn next(void) {
  tn k;
  cin >> k;
  return k;
}
template <typename tn>
inline ostream& operator<<(ostream& os, const vector<tn>& v) {
  for (register ll i = 0; i < v.size(); i++) os << v[i] << ' ';
  return os;
}
signed main(void) { return Solving(); }
