import random

def get_count(dim):
    current_square = [0 for i in range(dim)]
    visited_squares = [current_square]

    count = 0

    while True:
        all_movements = []
        for i in range(dim):
            new_square_1 = [current_square[j] for j in range(dim)]
            new_square_2 = [current_square[j] for j in range(dim)]
            new_square_1[i] += 1
            new_square_2[i] -= 1

            all_movements.append(new_square_1)
            all_movements.append(new_square_2)

        # list of possible squares to visit
        test_l = [i for i in all_movements if i not in visited_squares]

        if test_l == []:
            return count

        next_square = random.choice(test_l)

        if next_square not in visited_squares:
            current_square = next_square
            visited_squares.append(next_square)
            count += 1

def expected(d):
    total = float(sum(d[k] for k in d.keys()))
    result = 0

    for k in d.keys():
        result += k * (d[k] / total)
    return result

def variance(d):
    mu = expected(d)
    total = float(sum(d[k] for k in d.keys()))

    result = 0
    for k in d.keys():
        result += (d[k] / total) * (k - mu) ** 2
    return result


def analysis(dim):
    d = {}
    for i in range(1000):
        g = get_count(dim)
        if g not in d.keys():
            d[g] = 0
        d[g] += 1

    return [expected(d), variance(d)]

print analysis(2)