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 int arr[20009];
vector<long long int> vec, vec2;
int main() {
  long long int a, b, c, d, e, i, j, k, l, n, m, x, y, t, p;
  scanf("%lld", &t);
  for (p = 1; p <= t; p++) {
    scanf("%lld", &n);
    if (n == 1) {
      printf("FastestFinger\n");
    } else if (n == 2 || n % 2 == 1) {
      printf("Ashishgup\n");
    } else {
      a = 0;
      while (n % 2 == 0) {
        a++;
        n = n / 2;
      }
      if (n == 1) {
        printf("FastestFinger\n");
      } else {
        if (a > 1) {
          printf("Ashishgup\n");
        } else {
          m = sqrtl(n);
          c = 0;
          for (i = 2; i <= m; i++) {
            if (n % i == 0) {
              c = 1;
              break;
            }
          }
          if (c == 0) {
            printf("FastestFinger\n");
          } else {
            printf("Ashishgup\n");
          }
        }
      }
    }
  }
}
