from collections import defaultdict
import pprint
def build_graph(pairs):
    graph = defaultdict(list)
    for pair in pairs:
        a, b = map(int, pair.split('/'))
        graph[a].append(b)
        graph[b].append(a)
    return graph

def find_all_paths(graph, start, visited=None, path=None):
    if visited is None:
        visited = set()
    if path is None:
        path = []

    visited.add(start)
    path.append(start)

    paths = [list(path)]  # Store the current path as a possible connection

    for neighbor in graph[start]:
        if neighbor not in visited:
            paths.extend(find_all_paths(graph, neighbor, visited.copy(), path.copy()))

    return paths

def count_connections(pairs):
    graph = build_graph(pairs)
    all_paths = []

    for pair in pairs:
        a, b = map(int, pair.split('/'))
        paths_a = find_all_paths(graph, a)
        paths_b = find_all_paths(graph, b)
        
        # Combine paths starting from both nodes in the pair
        for path in paths_a:
            if b in path:
                all_paths.append(path)

        for path in paths_b:
            if a in path:
                all_paths.append(path)

    # Remove duplicate paths
    unique_paths = {tuple(path) for path in all_paths}
    return len(unique_paths), unique_paths

# Example usage
pairs = ['0/2','2/2','2/3','3/4','3/5','0/1','10/1','9/10']
connection_count, connections = count_connections(pairs)

print(f"Number of connections: {connection_count}")
print("Connections:")
for connection in connections:
    print(connection)
pprint(connections)