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;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t, n, d = 0, k = 0, x = 0, i = 0, m, f = 0, j = 0, c = 0,
                      sum = 0, s = 0;
  cin >> t;
  while (t--) {
    s = 0;
    sum = 0;
    cin >> m;
    f = m;
    while (m % 2 == 0) {
      m /= 2;
      s++;
    }
    for (j = 3; j * j <= m; j += 2) {
      while (m % j == 0) {
        m /= j;
        sum++;
      }
    }
    if (m > 1) {
      sum++;
    }
    if (f == 1) {
      j = 1;
    } else if (s == 0 && f != 1) {
      j = 0;
    } else if (s == 1) {
      if (sum > 1 or sum == 0) {
        j = 0;
      } else {
        j = 1;
      }
    } else {
      if (sum > 0) {
        j = 0;
      } else {
        j = 1;
      }
    }
    if (j == 1) {
      cout << "FastestFinger";
    } else {
      cout << "Ashishgup";
    }
    cout << endl;
  }
  return 0;
}
