5.5

# Continuation of ex 5.1's code

def lowerHull(points):
    points = sorted(points, key=lambda p: (p[0], p[1]))
    lower = []

    for p in points:
        while len(lower) >= 2 and orientation(Point(*lower[-2]), Point(*lower[-1]), Point(*p)) != 2:
            lower.pop()
        lower.append(p)

    return lower

input_points = [(1, 10), (-2, 7), (3, 8), (4, 10), (5, 7), (6, 7), (7, 11)]
lower_hull = lowerHull(input_points)

print("Lower Hull:")
for x, y in lower_hull:
    print(f"({x}, {y})")