# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

UpperCamelCase  							=						TypeVar('''T''')



class   snake_case_       (		Generic[T]       ):






   def __init__(      self				:     List[Any]	,						lowercase_				:     bool = True  )					->						None:
       lowercase__ :   dict[T, list[T]]    					=				{}  # dictionary of lists
       lowercase__ :   Union[str, Any]    					=				directed






   def       __UpperCamelCase     (      self				:     List[str]	,						lowercase_				:     T	,						lowercase_				:     T  )					->						GraphAdjacencyList[T]:

       if not self.directed:  # For undirected graphs
           # if both source vertex and destination vertex are both present in the
           # adjacency list, add destination vertex to source vertex list of adjacent
           # vertices and add source vertex to destination vertex list of adjacent
           # vertices.
           if source_vertex in self.adj_list and destination_vertex in self.adj_list:
               self.adj_list[source_vertex].append(lowercase_  )
               self.adj_list[destination_vertex].append(lowercase_  )
           # if only source vertex is present in adjacency list, add destination vertex
           # to source vertex list of adjacent vertices, then create a new vertex with
           # destination vertex as key and assign a list containing the source vertex
           # as it's first adjacent vertex.
           elif source_vertex in self.adj_list:
               self.adj_list[source_vertex].append(lowercase_  )
               lowercase__ :   List[str]    					=				[source_vertex]
           # if only destination vertex is present in adjacency list, add source vertex
           # to destination vertex list of adjacent vertices, then create a new vertex
           # with source vertex as key and assign a list containing the source vertex
           # as it's first adjacent vertex.
           elif destination_vertex in self.adj_list:
               self.adj_list[destination_vertex].append(lowercase_  )
               lowercase__ :   Optional[Any]    					=				[destination_vertex]
           # if both source vertex and destination vertex are not present in adjacency
           # list, create a new vertex with source vertex as key and assign a list
           # containing the destination vertex as it's first adjacent vertex also
           # create a new vertex with destination vertex as key and assign a list
           # containing the source vertex as it's first adjacent vertex.
           else:
               lowercase__ :   List[Any]    					=				[destination_vertex]
               lowercase__ :   List[Any]    					=				[source_vertex]
       else:  # For directed graphs
           # if both source vertex and destination vertex are present in adjacency
           # list, add destination vertex to source vertex list of adjacent vertices.
           if source_vertex in self.adj_list and destination_vertex in self.adj_list:
               self.adj_list[source_vertex].append(lowercase_  )
           # if only source vertex is present in adjacency list, add destination
           # vertex to source vertex list of adjacent vertices and create a new vertex
           # with destination vertex as key, which has no adjacent vertex
           elif source_vertex in self.adj_list:
               self.adj_list[source_vertex].append(lowercase_  )
               lowercase__ :   Optional[int]    					=				[]
           # if only destination vertex is present in adjacency list, create a new
           # vertex with source vertex as key and assign a list containing destination
           # vertex as first adjacent vertex
           elif destination_vertex in self.adj_list:
               lowercase__ :   Optional[int]    					=				[destination_vertex]
           # if both source vertex and destination vertex are not present in adjacency
           # list, create a new vertex with source vertex as key and a list containing
           # destination vertex as it's first adjacent vertex. Then create a new vertex
           # with destination vertex as key, which has no adjacent vertex
           else:
               lowercase__ :   Optional[Any]    					=				[destination_vertex]
               lowercase__ :   Optional[int]    					=				[]

       return self







   def __repr__(      self				:     Dict  )					->						str:
       return pformat(self.adj_list  )










from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       )      ->				list[int]:  # This function is recursive
   __snake_case							       =   len(snake_case_       )
   # If the array contains only one element, we return it (it's the stop condition of
   # recursion)
   if array_length <= 1:
      return array
      # Else
   __snake_case							       =   array[0]
   __snake_case							       =   False
   __snake_case							       =   1
   __snake_case							       =   []
   while not is_found and i < array_length:
      if array[i] < pivot:
         __snake_case							       =   True
         __snake_case							       =   [element for element in array[i:] if element >= array[i]]
         __snake_case							       =   longest_subsequence(snake_case_       )
         if len(snake_case_       ) > len(snake_case_       ):
            __snake_case							       =   temp_array
      else:
         i += 1

   __snake_case							       =   [element for element in array[1:] if element >= pivot]
   __snake_case							       =   [pivot, *longest_subsequence(snake_case_       )]
   if len(snake_case_       ) > len(snake_case_       ):
      return temp_array
   else:
      return longest_subseq


if __name__ == "__main__":
    import doctest

    doctest.testmod()

