human
What is a Python code to determine the winner of the game if both of them play optimally given the following:
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.
from
assistant
#Here is Python code to determine the winner of the game if both of them play optimally.
math import log

class Solution:
    def __init__(self):
        self.n = int(input())

    def solve_and_print(self):
        n = self.n
        if n == 1:
                print("FastestFinger")
        elif n == 2:
            print("Ashishgup")
        elif n%2 == 1:
            print("Ashishgup")
        elif log(n,2) - int(log(n,2)) == 0:
            print("FastestFinger")
        elif (n//2) % 2 == 0:
            print("Ashishgup")
        else:
            temp = n//2
            if self.isPrime(temp):
                print("FastestFinger")
            else:
                print("Ashishgup")
    def isPrime(self, n):
        if (n <= 1) : 
            return False
        if (n <= 3) : 
            return True
        if (n % 2 == 0 or n % 3 == 0) : 
            return False
        for i in range(5, int(n**0.5) + 1, 6) : 
            if (n % i == 0 or n % (i + 2) == 0) : 
                return False
        return True

if __name__ == "__main__":
    for _ in range(int(input())):
        Solution().solve_and_print()