

from __future__ import annotations

from typing import Generic, TypeVar

lowerCamelCase      				=     TypeVar('''T''')





class     snake_case_			(				Generic[T]							):


							"""simple docstring"""





							def __init__( self					,						_A							):
												__lowerCAmelCase					=							data
												__lowerCAmelCase					=							self
												__lowerCAmelCase					=							0





class     snake_case_			(				Generic[T]							):


							"""simple docstring"""





							def __init__( self							):
												# map from node name to the node object
												__lowerCAmelCase					=							{}




							def        A__  ( self					,						_A							):
												# create a new set with x as its member
												__lowerCAmelCase					=							DisjointSetTreeNode(_A							)




							def        A__  ( self					,						_A							):
												# find the set x belongs to (with path-compression)
												__lowerCAmelCase					=							self.map[data]
												if elem_ref != elem_ref.parent:
																	__lowerCAmelCase					=							self.find_set(elem_ref.parent.data							)
												return elem_ref.parent




							def        A__  ( self					,						_A					,						_A							):
												# helper function for union operation
												if nodea.rank > nodea.rank:
																	__lowerCAmelCase					=							nodea
												else:
																	__lowerCAmelCase					=							nodea
																	if nodea.rank == nodea.rank:
																						nodea.rank += 1




							def        A__  ( self					,						_A					,						_A							):
												# merge 2 disjoint sets
												self.link(self.find_set(_A							)					,						self.find_set(_A							)							)





class     snake_case_			(				Generic[T]							):


							"""simple docstring"""





							def __init__( self							):
												# connections: map from the node to the neighbouring nodes (with weights)
												__lowerCAmelCase					=							{}




							def        A__  ( self					,						_A							):
												# add a node ONLY if its not present in the graph
												if node not in self.connections:
																	__lowerCAmelCase					=							{}




							def        A__  ( self					,						_A					,						_A					,						_A							):
												# add an edge with the given weight
												self.add_node(_A							)
												self.add_node(_A							)
												__lowerCAmelCase					=							weight
												__lowerCAmelCase					=							weight




							def        A__  ( self							):
												__lowerCAmelCase					=							[]
												__lowerCAmelCase					=							set()
												for start in self.connections:
																	for end in self.connections[start]:
																						if (start, end) not in seen:
																											seen.add((end, start)							)
																											edges.append((start, end, self.connections[start][end])							)
												edges.sort(key=lambda _A							: x[2]							)

												# creating the disjoint set
												__lowerCAmelCase					=							DisjointSetTree[T]()
												for node in self.connections:
																	disjoint_set.make_set(_A							)

												# MST generation
												__lowerCAmelCase					=							0
												__lowerCAmelCase					=							0
												__lowerCAmelCase					=							GraphUndirectedWeighted[T]()
												while num_edges < len(self.connections							) - 1:
																	__lowerCAmelCase,	__lowerCAmelCase,	__lowerCAmelCase					=							edges[index]
																	index += 1
																	__lowerCAmelCase					=							disjoint_set.find_set(_A							)
																	__lowerCAmelCase					=							disjoint_set.find_set(_A							)
																	if parent_u != parent_v:
																						num_edges += 1
																						graph.add_edge(_A					,						_A					,						_A							)
																						disjoint_set.union(_A					,						_A							)
												return graph









def        __lowercase    (  UpperCAmelCase__		,					UpperCAmelCase__      ):

					"""simple docstring"""






					assert x is not None
					assert y is not None

					__lowerCAmelCase					=							len(UpperCAmelCase__      )
					__lowerCAmelCase					=							len(UpperCAmelCase__      )

					# declaring the array for storing the dp values
					__lowerCAmelCase					=							[[0] * (n + 1) for _ in range(m + 1      )]  # noqa: E741

					for i in range(1		,					m + 1      ):
										for j in range(1		,					n + 1      ):
															__lowerCAmelCase					=							1 if x[i - 1] == y[j - 1] else 0

															__lowerCAmelCase					=							max(l[i - 1][j]		,					l[i][j - 1]		,					l[i - 1][j - 1] + match      )

					__lowerCAmelCase					=							''
					__lowerCAmelCase,	__lowerCAmelCase					=							m, n
					while i > 0 and j > 0:
										__lowerCAmelCase					=							1 if x[i - 1] == y[j - 1] else 0

										if l[i][j] == l[i - 1][j - 1] + match:
															if match == 1:
																				__lowerCAmelCase					=							x[i - 1] + seq
															i -= 1
															j -= 1
										elif l[i][j] == l[i - 1][j]:
															i -= 1
										else:
															j -= 1

					return l[m][n], seq


if __name__ == "__main__":
		lowerCamelCase      				=     '''AGGTAB'''
		lowerCamelCase      				=     '''GXTXAYB'''
		lowerCamelCase      				=     4
		lowerCamelCase      				=     '''GTAB'''

		lowerCamelCase				,				lowerCamelCase      				=     longest_common_subsequence(a, b)
		print('''len =''', ln, ''', sub-sequence =''', subseq)
		import doctest

		doctest.testmod()






