<｜begin▁of▁sentence｜>### Instruction:
Imagine you're a hydroponic farmer overseeing a complex irrigation system for your plants, designed to efficiently distribute water and nutrients. The system's layout resembles a directed acyclic graph (DAG) where each node represents a junction, and the directed edges symbolize the one-way flow of the nutrient mixture from one junction to another. Your system consists of junctions numbered [0, 1, 2, 3], and the flow paths are configured as [(0, 1), (0, 3), (1, 2)].

Now, to optimize and troubleshoot the delivery, you need to understand the relationship between different junctions in your irrigation network. Specifically, you want to find the "lowest common junction" from which nutrients flow to reach any two given junctions within the system.

For the entire network, you're aiming to map out the lowest common junction for every possible pair of junctions. Moreover, you’re particularly interested in determining the lowest common junctions for the pairs (1, 2) and (2, 3) to ensure that these junctions receive an adequate supply.

Can you devise a method within the existing layout to identify these critical points of origin in your nutrient distribution system?
### Response:
import networkx as nx

# Create a directed acyclic graph (DAG)
G = nx.DiGraph([(0, 1), (0, 3), (1, 2)])

# Compute the lowest common ancestor for all pairs
# Convert the generator to a dictionary for better visualization
lca_all_pairs = dict(nx.all_pairs_lowest_common_ancestor(G))

print('All pairs lowest common ancestor:')
print(lca_all_pairs)

# Now compute the LCA for specific pairs
specific_pairs = [(1, 2), (2, 3)]
lca_specific_pairs = dict(nx.all_pairs_lowest_common_ancestor(G, pairs=specific_pairs))

print('\nSpecific pairs lowest common ancestor:')
print(lca_specific_pairs)
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