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;
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long mpow(long long base, long long exp);
void ipgraph(long long m);
const long long mod = 1000000007;
const long long N = 1000000001;
const long long MAX = 1e9 + 1;
template <typename... T>
void in(T &...args) {
  ((cin >> args), ...);
}
template <typename... T>
void out(T &&...args) {
  ((cout << args << " "), ...);
}
template <typename... T>
void outl(T &&...args) {
  ((cout << args << "\n"), ...);
}
long long fast_exp(long long base, long long exp) {
  long long res = 1;
  while (exp > 0) {
    if (exp % 2 == 1) res = (res * base);
    base = (base * base);
    exp /= 2;
  }
  return res;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t;
  in(t);
  while (t--) {
    long long n;
    in(n);
    long long p = n;
    while (p % 2 == 0) p = p / 2;
    if (n == 1) {
      cout << "FastestFinger"
           << "\n";
      continue;
    }
    if (n % 2 == 1) {
      outl("Ashishgup");
      continue;
    } else if (n == 2) {
      cout << "Ashishgup"
           << "\n";
    } else if ((n & (n - 1)) == 0) {
      cout << "FastestFinger"
           << "\n";
    } else {
      n = n / 2;
      long long flag = 0;
      for (long long i = 2; i * i <= n; i++) {
        if (n % i == 0) {
          flag = 1;
          break;
        }
      }
      if (flag) {
        cout << "Ashishgup"
             << "\n";
      } else {
        cout << "FastestFinger"
             << "\n";
      }
    }
  }
  return 0;
}
