


"""simple docstring"""







import numpy as np

lowerCamelCase_       :       Union[str, Any]      						=  [
    ["""a""", """b""", """c""", """d""", """e"""],
    ["""f""", """g""", """h""", """i""", """k"""],
    ["""l""", """m""", """n""", """o""", """p"""],
    ["""q""", """r""", """s""", """t""", """u"""],
    ["""v""", """w""", """x""", """y""", """z"""],
]






class 				__A    :






 """simple docstring"""




 def __init__(		self						) ->					None:
     a					=np.array(__A						)


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					np.ndarray:
     a		,				a					=np.where(letter == self.SQUARE						)
     a					=np.concatenate([indexa + 1, indexa + 1]						)
     return indexes


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					str:
     a					=self.SQUARE[indexa - 1, indexa - 1]
     return letter


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					str:
     a					=message.lower()
     a					=message.replace(''' '''			,   ''''''						)
     a					=message.replace('''j'''			,   '''i'''						)

     a					=np.empty((2, len(__A						))						)
     for letter_index in range(len(__A						)						):
         a					=self.letter_to_numbers(message[letter_index]						)

         a					=numbers[0]
         a					=numbers[1]

     a					=first_step.reshape(2 * len(__A						)						)
     a					=''''''
     for numbers_index in range(len(__A						)						):
         a					=int(second_step[numbers_index * 2]						)
         a					=int(second_step[(numbers_index * 2) + 1]						)
         a					=self.numbers_to_letter(__A			,   __A						)
         a					=encoded_message + letter

     return encoded_message





 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					str:
     a					=message.lower()
     message.replace(''' '''			,   ''''''						)
     a					=np.empty(2 * len(__A						)						)
     for letter_index in range(len(__A						)						):
         a					=self.letter_to_numbers(message[letter_index]						)
         a					=numbers[0]
         a					=numbers[1]

     a					=first_step.reshape((2, len(__A						))						)
     a					=''''''
     for numbers_index in range(len(__A						)						):
         a					=int(second_step[0, numbers_index]						)
         a					=int(second_step[1, numbers_index]						)
         a					=self.numbers_to_letter(__A			,   __A						)
         a					=decoded_message + letter

     return decoded_message



"""simple docstring"""







from __future__ import annotations

from typing import Generic, TypeVar

lowerCamelCase_       :       List[Any]      						=  TypeVar("""T""")






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self			,   __A						) ->					None:
     a					=data
     a					=self
     a					=0






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # map from node name to the node object
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # create a new set with x as its member
     a					=DisjointSetTreeNode(__A						)


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					DisjointSetTreeNode[T]:
     # find the set x belongs to (with path-compression)
     a					=self.map[data]
     if elem_ref != elem_ref.parent:
         a					=self.find_set(elem_ref.parent.data						)
     return elem_ref.parent


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # helper function for union operation
     if nodea.rank > nodea.rank:
         a					=nodea
     else:
         a					=nodea
         if nodea.rank == nodea.rank:
             nodea.rank += 1





 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # merge 2 disjoint sets
     self.link(self.find_set(__A						)			,   self.find_set(__A						)						)






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # connections: map from the node to the neighbouring nodes (with weights)
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # add a node ONLY if its not present in the graph
     if node not in self.connections:
         a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A			,   __A						) ->					None:
     # add an edge with the given weight
     self.add_node(__A						)
     self.add_node(__A						)
     a					=weight
     a					=weight





 def 				SCREAMING_SNAKE_CASE							(		self						) ->					GraphUndirectedWeighted[T]:
     a					=[]
     a					=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
     a					=DisjointSetTree[T]()
     for node in self.connections:
         disjoint_set.make_set(__A						)

     # MST generation
     a					=0
     a					=0
     a					=GraphUndirectedWeighted[T]()
     while num_edges < len(self.connections						) - 1:
         a		,				a		,				a					=edges[index]
         index += 1
         a					=disjoint_set.find_set(__A						)
         a					=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