




def       UpperCAmelCase       (     _snake_case							):

							if not grid or not grid[0]:
														raise TypeError('''The grid does not contain the appropriate information'''							)

							for cell_n in range(1						, len(grid[0]							)							):
														grid[0][cell_n] += grid[0][cell_n - 1]
							lowerCAmelCase   =		grid[0]

							for row_n in range(1						, len(_snake_case							)							):
														lowerCAmelCase   =		grid[row_n]
														lowerCAmelCase   =		fill_row(_snake_case						, _snake_case							)
														lowerCAmelCase   =		grid[row_n]

							return grid[-1][-1]



def       UpperCAmelCase       (     _snake_case						, _snake_case							):
							current_row[0] += row_above[0]
							for cell_n in range(1						, len(_snake_case							)							):
														current_row[cell_n] += min(current_row[cell_n - 1]						, row_above[cell_n]							)

							return current_row


if __name__ == "__main__":
		import doctest

		doctest.testmod()









from __future__ import annotations

from typing import Generic, TypeVar

UpperCAmelCase_						=TypeVar("""T""")


class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



				def __init__( self       , UpperCAmelCase_						):
											lowerCAmelCase   =		data
											lowerCAmelCase   =		self
											lowerCAmelCase   =		0




class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



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



				def       __snake_case		( self       , UpperCAmelCase_						):
											# create a new set with x as its member
											lowerCAmelCase   =		DisjointSetTreeNode(UpperCAmelCase_						)



				def       __snake_case		( self       , UpperCAmelCase_						):
											# 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       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_						):
											# helper function for union operation
											if nodea.rank > nodea.rank:
																		lowerCAmelCase   =		nodea
											else:
																		lowerCAmelCase   =		nodea
																		if nodea.rank == nodea.rank:
																									nodea.rank += 1






				def       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_						):
											# merge 2 disjoint sets
											self.link(self.find_set(UpperCAmelCase_						)       , self.find_set(UpperCAmelCase_						)						)




class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



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



				def       __snake_case		( self       , UpperCAmelCase_						):
											# add a node ONLY if its not present in the graph
											if node not in self.connections:
																		lowerCAmelCase   =		{}



				def       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_       , UpperCAmelCase_						):
											# add an edge with the given weight
											self.add_node(UpperCAmelCase_						)
											self.add_node(UpperCAmelCase_						)
											lowerCAmelCase   =		weight
											lowerCAmelCase   =		weight






				def       __snake_case		( 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 UpperCAmelCase_						: x[2]						)

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

											# 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(UpperCAmelCase_						)
																		lowerCAmelCase   =		disjoint_set.find_set(UpperCAmelCase_						)
																		if parent_u != parent_v:
																									num_edges += 1
																									graph.add_edge(UpperCAmelCase_       , UpperCAmelCase_       , UpperCAmelCase_						)
																									disjoint_set.union(UpperCAmelCase_       , UpperCAmelCase_						)
											return graph



