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 ms = 1e5 + 10;
bool notPrime[ms];
long long primes[ms], qnt;
void sieve(long long lim) {
  for (long long i = 2; i < ms; i++) {
    if (notPrime[i]) continue;
    primes[qnt++] = i;
    for (long long j = i + i; j < ms; j += i) notPrime[j] = true;
  }
}
void solve() {
  long long n;
  cin >> n;
  if (n == 1) {
    cout << "FastestFinger" << endl;
    return;
  }
  if (n == 2) {
    cout << "Ashishgup" << endl;
    return;
  }
  if (n & 1) {
    cout << "Ashishgup" << endl;
    return;
  }
  long long dois = 0;
  long long imp = 0;
  long long at = n;
  for (long long i = 0; i < qnt && primes[i] <= n; i++) {
    while (at % primes[i] == 0) {
      at /= primes[i];
      if (i == 0)
        dois++;
      else
        imp++;
    }
    if (at == 1) break;
  }
  if (at != 1) imp++;
  if (imp == 0) {
    cout << "FastestFinger" << endl;
    return;
  }
  if (dois == 1 && imp == 1) {
    cout << "FastestFinger" << endl;
    return;
  }
  cout << "Ashishgup" << endl;
  return;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  sieve(1e5);
  long long tc = 1;
  cin >> tc;
  while (tc--) solve();
}
