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;
const ll n_ = 1e6 + 10, inf = 1e18, mod = 1e9 + 7;
ll n, m, a, b, c, d, x, y, t, k, u, h;
ll dp[n_];
bool isprime(ll x) {
  for (ll i = 2; i * i <= x; i++)
    if ((x % i) == 0) return false;
  return true;
}
void solve() {
  ll ans = 0;
  cin >> n;
  bool ok = true;
  if (n == 1 || n == 2)
    ok = n == 2 ? 1 : 0;
  else if (n % 2)
    ok = true;
  else {
    a = n;
    while (a % 2 == 0) a /= 2;
    if (a == 1) ok = false;
    n /= 2;
    if (isprime(n)) ok = false;
  }
  if (ok)
    cout << "Ashishgup" << '\n';
  else
    cout << "FastestFinger" << '\n';
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  cin >> t;
  while (t--) solve();
}
