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 math import ceil, sqrt


def sieve(n):
    sqrtn = ceil(sqrt(n))
    prime = [True for _ in range(n + 1)]

    p = 2
    while p <= sqrtn:
        if prime[p]:
            for i in range(p * 2, n + 1, p):
                prime[i] = False
        p += 1

    prime[0] = False
    prime[1] = False

    return [i for i, x in enumerate(prime) if x]


if __name__ == '__main__':
    primes = sieve(10 ** 5)
    for _ in range(int(input())):
        n = int(input())

        if n == 1:
            print('FastestFinger')
        elif n % 2:
            print('Ashishgup')
        else:
            hp = 0

            while not n % 2:
                n //= 2
                hp += 1

            if hp == 1:
                if n == 1:
                    print('Ashishgup')
                elif n in primes or not len(list(filter(lambda o: not n % o, primes))):
                    print('FastestFinger')
                else:
                    print('Ashishgup')

            elif n == 1:
                print('FastestFinger')
            else:
                print('Ashishgup')
