#include <bits/stdc++.h>
using namespace std;
int pop_count(int u) {
  int ret = 0;
  while (u) {
    u = (u & (u - 1));
    ret++;
  }
  return ret;
}
bool Pr(int x) {
  if (x <= 1) return 0;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) return 0;
  }
  return 1;
}
int cnt = 0;
int n;
int main() {
  int T;
  cin >> T;
  while (T--) {
    cin >> n;
    if (n == 1) {
      puts("FastestFinger");
    } else if (n == 2) {
      puts("Ashishgup");
    } else if (n % 2 == 1) {
      puts("Ashishgup");
    } else if (pop_count(n) == 1) {
      puts("FastestFinger");
    } else if (n % 4 == 0) {
      puts("Ashishgup");
    } else {
      n /= 2;
      if (Pr(n))
        puts("FastestFinger");
      else
        puts("Ashishgup");
    }
  }
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int pop_count(int u) {
  int ret = 0;
  while (u) {
    u = (u & (u - 1));
    ret++;
  }
  return ret;
}
bool Pr(int x) {
  if (x <= 1) return 0;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) return 0;
  }
  return 1;
}
int cnt = 0;
int n;
int main() {
  int T;
  cin >> T;
  while (T--) {
    cin >> n;
    if (n == 1) {
      puts("FastestFinger");
    } else if (n == 2) {
      puts("Ashishgup");
    } else if (n % 2 == 1) {
      puts("Ashishgup");
    } else if (pop_count(n) == 1) {
      puts("FastestFinger");
    } else if (n % 4 == 0) {
      puts("Ashishgup");
    } else {
      n /= 2;
      if (Pr(n))
        puts("FastestFinger");
      else
        puts("Ashishgup");
    }
  }
  return 0;
}

```