def define_epsilon():
    eps = 1.0
    while eps + 1 > 1:
        eps /= 2
    eps *= 2
    return eps


def is_between(a, b, c):
    epsilon = define_epsilon()
    cross_product = (c[1] - a[1]) * (b[0] - a[0]) - (c[0] - a[0]) * (b[1] - a[1])

    # compare versus epsilon for floating point values, or != 0 if using integers
    if abs(cross_product) > epsilon:
        return False

    dot_product = (c[0] - a[0]) * (b[0] - a[0]) + (c[1] - a[1]) * (b[1] - a[1])
    if dot_product < 0:
        return False

    squared_length_b_a = (b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1])
    if dot_product > squared_length_b_a:
        return False

    return True


def checkio(cakes):
    lines = []
    count_cakes = len(cakes)
    i = 0
    while i <= count_cakes - 1:
        first_cake = cakes[i]
        j = 0
        while j <= count_cakes - 1:
            if j <= i:
                j += 1
                continue
            second_cake = cakes[j]
            k = 0
            while k <= count_cakes - 1:
                if k == i or k == j:
                    k += 1
                    continue
                third_cake = cakes[k]
                if is_between(first_cake, second_cake, third_cake):
                    line_to_add = [first_cake, second_cake, third_cake]
                    for line in lines:
                        count = 0
                        to_add = []
                        if first_cake in line:
                            count += 1
                        else:
                            to_add.append(first_cake)
                        if second_cake in line:
                            count += 1
                        else:
                            to_add.append(second_cake)
                        if third_cake in line:
                            count += 1
                        else:
                            to_add.append(third_cake)
                        if count >= 2:
                            line_to_add = None
                            for t in to_add:
                                line.append(t)

                    if line_to_add is not None:
                        lines.append(line_to_add)
                k += 1
            j += 1
        i += 1

    print(lines)
    return len(lines)


# These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
    assert checkio([[3, 3], [5, 5], [8, 8], [2, 8], [8, 2]]) == 2
    assert checkio(
        [[2, 2], [2, 5], [2, 8], [5, 2], [7, 2], [8, 2],
         [9, 2], [4, 5], [4, 8], [7, 5], [5, 8], [9, 8]]) == 6