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;
const int maxn = 1e5 + 5;
inline int isPrime(int n) {
  int ele1 = sqrt(n);
  for (int i = 2; i <= ele1; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
int main() {
  int num;
  scanf("%d", &num);
  while (num--) {
    int ele;
    scanf("%d", &ele);
    if ((ele & 1) == 1) {
      if (ele == 1)
        printf("FastestFinger\n");
      else
        printf("Ashishgup\n");
    } else if (ele == 2)
      printf("Ashishgup\n");
    else {
      int n = sqrt(ele);
      int flag = 0;
      int ele1 = ele / 2;
      if (ele1 % 2 == 1) {
        flag = isPrime(ele1);
        if (flag) {
          printf("FastestFinger\n");
        } else
          printf("Ashishgup\n");
      } else {
        for (int i = 2; i <= n; i++) {
          if (ele % i == 0) {
            int a1 = ele / i;
            if (a1 % 2 == 1 || i % 2 == 1) {
              flag = 1;
              break;
            }
          }
        }
        if (flag == 1)
          printf("Ashishgup\n");
        else
          printf("FastestFinger\n");
      }
    }
  }
}
