




class 			lowerCamelCase_				:


 '''simple docstring'''







 def __init__(				self    :						str		):
       SCREAMING_SNAKE_CASE_      		=     {}



 def  lowerCAmelCase_    (				self    :						List[str]		):
       print(self.vertex		)
       for i in self.vertex:
             print(_lowerCAmelCase							,							' -> '							,							' -> '.join([str(_lowerCAmelCase		) for j in self.vertex[i]]		)		)



 def  lowerCAmelCase_    (				self    :						Union[str, Any]							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						int		):
       # check if vertex is already present,
       if from_vertex in self.vertex:
             self.vertex[from_vertex].append(_lowerCAmelCase		)
       else:
             # else make a new vertex
             SCREAMING_SNAKE_CASE_      		=     [to_vertex]



 def  lowerCAmelCase_    (				self    :						Optional[Any]		):
       # visited array for storing already visited nodes
       SCREAMING_SNAKE_CASE_      		=     [False] * len(self.vertex		)

       # call the recursive helper function
       for i in range(len(self.vertex		)		):
             if not visited[i]:
                   self.dfs_recursive(_lowerCAmelCase							,							_lowerCAmelCase		)




 def  lowerCAmelCase_    (				self    :						Tuple							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						list		):
       # mark start vertex as visited
       SCREAMING_SNAKE_CASE_      		=     True

       print(_lowerCAmelCase							,							end=' '		)

       # Recur for all the vertices that are adjacent to this node
       for i in self.vertex:
             if not visited[i]:
                   self.dfs_recursive(_lowerCAmelCase							,							_lowerCAmelCase		)


if __name__ == "__main__":
   lowerCamelCase__					:  List[Any]      							=				Graph()
   g.add_edge(0, 1)
   g.add_edge(0, 2)
   g.add_edge(1, 2)
   g.add_edge(2, 0)
   g.add_edge(2, 3)
   g.add_edge(3, 3)

   g.print_graph()
   print('DFS:')
   g.dfs()

   # OUTPUT:
   # 0  ->  1 -> 2
   # 1  ->  2
   # 2  ->  0 -> 3
   # 3  ->  3
   # DFS:
   #  0 1 2 3





def    UpperCAmelCase_				( )   ->					list[list[int]]:
      return [list(range(10_00 - i     ,     -10_00 - i     ,     -1				)				) for i in range(10_00				)]


lowerCamelCase__					:  List[Any]      							=				generate_large_matrix()
lowerCamelCase__					:  List[Any]      							=				(
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list[int]]				)   ->					None:
      assert all(row == sorted(__UpperCAmelCase     ,     reverse=__UpperCAmelCase				) for row in grid				)
      assert all(list(__UpperCAmelCase				) == sorted(__UpperCAmelCase     ,     reverse=__UpperCAmelCase				) for col in zip(*__UpperCAmelCase				)				)

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[int]				)   ->					int:
      SCREAMING_SNAKE_CASE_      		=     0
      SCREAMING_SNAKE_CASE_      		=     len(__UpperCAmelCase				) - 1

      # Edge cases such as no values or all numbers are negative.
      if not array or array[0] < 0:
            return 0

      while right + 1 > left:
            SCREAMING_SNAKE_CASE_      		=     (left + right) // 2
            SCREAMING_SNAKE_CASE_      		=     array[mid]

            # Num must be negative and the index must be greater than or equal to 0.
            if num < 0 and array[mid - 1] >= 0:
                  return mid

            if num >= 0:
                  SCREAMING_SNAKE_CASE_      		=     mid + 1
            else:
                  SCREAMING_SNAKE_CASE_      		=     mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
      return len(__UpperCAmelCase				)

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list[int]]				)   ->					int:
      SCREAMING_SNAKE_CASE_      		=     0
      SCREAMING_SNAKE_CASE_      		=     len(grid[0]				)

      for i in range(len(__UpperCAmelCase				)				):
            SCREAMING_SNAKE_CASE_      		=     find_negative_index(grid[i][:bound]				)
            total += bound
      return (len(__UpperCAmelCase				) * len(grid[0]				)) - total

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list[int]]				)   ->					int:
      return len([number for row in grid for number in row if number < 0]				)

def    UpperCAmelCase_				( __UpperCAmelCase		:      list[list[int]]				)   ->					int:
      SCREAMING_SNAKE_CASE_      		=     0
      for row in grid:
            for i, number in enumerate(__UpperCAmelCase				):
                  if number < 0:
                        total += len(__UpperCAmelCase				) - i
                        break
      return total

def    UpperCAmelCase_				( )   ->					None:
      from timeit import timeit

      print('Running benchmarks'				)
      SCREAMING_SNAKE_CASE_      		=     (
          'from __main__ import count_negatives_binary_search, '
          'count_negatives_brute_force, count_negatives_brute_force_with_break, grid'
      )
      for func in (
          "count_negatives_binary_search",  # took 0.7727 seconds
          "count_negatives_brute_force_with_break",  # took 4.6505 seconds
          "count_negatives_brute_force",  # took 12.8160 seconds
      ):
            SCREAMING_SNAKE_CASE_      		=     timeit(f"{func}(grid=grid)"     ,     setup=__UpperCAmelCase     ,     number=5_00				)
            print(f"{func}() took {time:0.4f} seconds"				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()