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;
void func(void) {
  freopen("input.c", "r", stdin);
  freopen("output.c", "w", stdout);
}
void print(vector<long long> &v) {
  cout << v.size() << endl;
  for (int i = 0; i < v.size(); i++) {
    printf("%lld ", v[i]);
  }
  printf("\n");
}
void print(vector<pair<long long, long long> > &v) {
  cout << v.size() << endl;
  for (int i = 0; i < v.size(); i++) {
    printf("%lld %lld\n", v[i].first, v[i].second);
  }
}
void print(double d) { cout << fixed << setprecision(10) << d << endl; }
void print(string s, double d) {
  cout << s << " ";
  cout << fixed << setprecision(10) << d << endl;
}
int main() {
  long long n, q, i, j = 0, temp, t, k, ans = 0, sum = 0, x, y, z, cnt = 0, m,
                     fg = 0, mx = 0, mx1 = 0, mn = 8000000000000000000,
                     mn1 = 8000000000000000000;
  cin >> t;
  while (t--) {
    cin >> n;
    string s1 = "Ashishgup";
    string s2 = "FastestFinger";
    if (n == 1) {
      cout << s2 << endl;
      continue;
    }
    if (n == 2) {
      cout << s1 << endl;
      continue;
    }
    if (n % 2 == 1) {
      cout << s1 << endl;
      continue;
    }
    long long even = 0;
    while (n % 2 == 0) {
      n /= 2;
      even++;
    }
    long long odd = 0;
    for (int i = 3; i < 100000; i += 2) {
      while (n % i == 0) {
        n /= i;
        odd++;
      }
    }
    if (n != 1) odd++;
    if ((odd == 1 and even == 1) or odd == 0) {
      cout << s2 << endl;
      continue;
    }
    cout << s1 << endl;
  }
}
