





'''simple docstring'''


from __future__ import annotations
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			int = 4 )							->     list[list[int]]:

       """simple docstring"""


       UpperCAmelCase  =						abs(SCREAMING_SNAKE_CASE_ ) or 4
       return [[1 + x + y * row_size for x in range(SCREAMING_SNAKE_CASE_ )] for y in range(SCREAMING_SNAKE_CASE_ )]
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       return reverse_row(transpose(SCREAMING_SNAKE_CASE_ ) )
       # OR.. transpose(reverse_column(matrix))
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       return reverse_row(reverse_column(SCREAMING_SNAKE_CASE_ ) )
       # OR.. reverse_column(reverse_row(matrix))
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       return reverse_column(transpose(SCREAMING_SNAKE_CASE_ ) )
       # OR.. transpose(reverse_row(matrix))
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       UpperCAmelCase  =						[list(SCREAMING_SNAKE_CASE_ ) for x in zip(*SCREAMING_SNAKE_CASE_ )]
       return matrix
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       UpperCAmelCase  =						matrix[::-1]
       return matrix
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     list[list[int]]:

       """simple docstring"""


       UpperCAmelCase  =						[x[::-1] for x in matrix]
       return matrix
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			list[list[int]] )							->     None:

       """simple docstring"""


       for i in matrix:
              print(*SCREAMING_SNAKE_CASE_ )


if __name__ == "__main__":
    a__			:					str       						=						make_matrix()
    print('\norigin:\n')
    print_matrix(matrix)
    print('\nrotate 90 counterclockwise:\n')
    print_matrix(rotate_aa(matrix))

    a__			:					List[str]       						=						make_matrix()
    print('\norigin:\n')
    print_matrix(matrix)
    print('\nrotate 180:\n')
    print_matrix(rotate_aaa(matrix))

    a__			:					Union[str, Any]       						=						make_matrix()
    print('\norigin:\n')
    print_matrix(matrix)
    print('\nrotate 270 counterclockwise:\n')
    print_matrix(rotate_aaa(matrix))





from collections import deque





def      A__					(			__A  :						Optional[Any]			)					->Tuple:
      __A    =len(__A			)
      __A    =deque()
      __A    =[False for _ in range(__A			)]
      __A    =[-1 for _ in range(__A			)]
      __A    =index_of[:]

      def strong_connect(__A  :						Union[str, Any]     ,				__A  :						int     ,				__A  :						Optional[int]			):
            __A    =index  # the number when this node is seen
            __A    =index  # lowest rank node reachable from here
            index += 1
            stack.append(__A			)
            __A    =True

            for w in g[v]:
                  if index_of[w] == -1:
                        __A    =strong_connect(__A     ,				__A     ,				__A			)
                        __A    =(
                            lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
                        )
                  elif on_stack[w]:
                        __A    =(
                            lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
                        )

            if lowlink_of[v] == index_of[v]:
                  __A    =[]
                  __A    =stack.pop()
                  __A    =False
                  component.append(__A			)
                  while w != v:
                        __A    =stack.pop()
                        __A    =False
                        component.append(__A			)
                  components.append(__A			)
            return index

      __A    =[]
      for v in range(__A			):
            if index_of[v] == -1:
                  strong_connect(__A     ,				0     ,				__A			)

      return components





def      A__					(			__A  :						List[Any]     ,				__A  :						Optional[int]			)					->Tuple:
      __A    =[[] for _ in range(__A			)]
      for u, v in edges:
            g[u].append(__A			)
      return g


if __name__ == "__main__":
   # Test
   _lowerCamelCase      :					int					    =      7
   _lowerCamelCase      :					Tuple					    =      [0, 0, 1, 2, 3, 3, 4, 4, 6]
   _lowerCamelCase      :					Dict					    =      [1, 3, 2, 0, 1, 4, 5, 6, 5]
   _lowerCamelCase      :					Optional[Any]					    =      [(u, v) for u, v in zip(source, target)]
   _lowerCamelCase      :					Dict					    =      create_graph(n_vertices, edges)

   assert [[5], [6], [4], [3, 2, 1, 0]] == tarjan(g)


