<｜begin▁of▁sentence｜>### Instruction:
Imagine you're in a workshop, crafting a collection of custom-designed furniture sets. You've got two distinct sets of components: set U, which includes the framework parts labeled 1, 2, 3, and 4, and set V, which consists of the unique design elements labeled 'a', 'b', 'c', and 'd'. You've already started combining some of them, forging connections (or edges) like so: framework part 1 with design elements 'a' and 'b'; 2 with 'a' and 'c'; 3 with 'c'; and 4 with 'a' and 'd'.

Your goal is to create a series of furniture sets where each framework part is matched perfectly with one design element, ensuring that no single piece is left out and every set is unique and complete. But you wonder, what's the greatest number of sets you can craft before adding any more would prevent you from achieving this perfect harmony between the components?
### Response:
import networkx as nx
from networkx.algorithms.matching import maximal_matching
from networkx.algorithms.bipartite.matching import hopcroft_karp_matching

# Create a bipartite graph
B = nx.Graph()
B.add_nodes_from([1, 2, 3, 4], bipartite=0) # Add the node attribute "bipartite"
B.add_nodes_from(['a', 'b', 'c', 'd'], bipartite=1)
B.add_edges_from([(1, 'a'), (1, 'b'), (2, 'a'), (2, 'c'), (3, 'c'), (4, 'a'), (4, 'd')])

# Check if the graph is bipartite and connected
if nx.is_connected(B) and nx.is_bipartite(B):
    try:
        # Find a perfect matching
        matching = hopcroft_karp_matching(B)
        if len(matching) == len(B) // 2: # Ensure the matching is perfect
            extendability = nx.maximal_extendability(B)
            print("The maximal extendability of the graph is:", extendability)
        else:
            print("The graph does not contain a perfect matching.")
    except nx.NetworkXError as e:
        print("An error occurred:", e)
else:
    print("The graph is either not connected or not bipartite.")
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