code_jam_BFF

def find_max_circle(next_items):
    visited = {}
    max_circle = 0

    for current in next_items:
        if current in visited:
            continue

        path = []
        p = current
        while p not in visited:
            path.append(p)
            visited[p] = True
            p = next_items[p]

        if p in path:
            circle = len(path) - path.index(p)
            max_circle = max(max_circle, circle)

    return max_circle


def find_tree_height(node, root, node_children, exclude=None):
    if node is None or node == exclude:
        return 0

    max_child_height = 0
    for child in node_children[node]:
        if child is not root:
            max_child_height = max(max_child_height, find_tree_height(child, root, node_children, exclude))

    return 1 + max_child_height


def get_node_children(next_items):
    node_children = []
    for current in range(len(next_items)):
        children = []
        for child, parent in enumerate(next_items):
            if parent == current:
                children.append(child)
        node_children.append(children)

    return node_children


def get_partitions(next_items):
    for current, depends_on in enumerate(next_items):
        if current == next_items[depends_on]:
            if current < depends_on:
                yield (current, depends_on)


def get_total_partition_width(next_items):
    node_children = get_node_children(next_items)
    partitions = get_partitions(next_items)
    total = 0

    for partition in partitions:
        total += find_tree_height(partition[0], partition[0], node_children, partition[1])
        total += find_tree_height(partition[1], partition[1], node_children, partition[0])

    return total


def solve(items):
    return max(find_max_circle(items), get_total_partition_width(items))


file = open('input3a')

index = 0
for line in file.readlines():
    if index != 0 and index % 2 == 0:
        answer = solve([int(s) - 1 for s in line.strip().split()])
        print('Case #%s: %i' % (index // 2, answer))
    index += 1
file.close()