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.
assistant
#Here is Python code to determine the winner of the game if both of them play optimally.

import math
for _ in range(int(input())):
    n = int(input())
    c = 0
    def is_prime_number(x):
        for i in range(2,int(math.sqrt(x))+1):
            if x%i == 0:
                return False
        return True
    while(n%2 == 0):
        n = n//2
        c +=1

    if n > 1 and c == 0:
        print('Ashishgup')
    elif n == 1 and c < 2:
        if c == 1:
            print('Ashishgup')
        elif n == 1 and c == 0:
            print('FastestFinger')

    elif n == 1 and c > 1:
        print('FastestFinger')

    elif n> 1 and c == 1 :
        if is_prime_number(n):
            
            print('FastestFinger')
        else:
            print('Ashishgup')
    elif n>1 and c > 1:
        print('Ashishgup')