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>
bool compare(int a, int b) { return a < b; }
void swapped(char s1, char s2) {
  char temp = s1;
  s1 = s2;
  s2 = temp;
}
long long int modd(long long int n, long long int k) {
  return (k + (n % k)) % k;
}
bool i(long long first) { return first && (!(first & (first - 1))); }
bool p(long long n) {
  long long i, flag = 1;
  for (i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      flag = 0;
      break;
    }
  }
  if (flag == 1) {
    return true;
  } else {
    return false;
  }
  return 0;
}
using namespace std;
void solve() {
  long long n;
  cin >> n;
  if (n == 1) {
    cout << "FastestFinger" << '\n';
    return;
  }
  if (n == 2) {
    cout << "Ashishgup" << '\n';
    return;
  }
  if (i(n)) {
    cout << "FastestFinger" << '\n';
    return;
  }
  if (n & 1) {
    cout << "Ashishgup" << '\n';
    return;
  }
  n /= 2;
  if (p(n)) {
    cout << "FastestFinger" << '\n';
    return;
  } else {
    cout << "Ashishgup" << '\n';
    return;
  }
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
