

'''simple docstring'''






def 		_A     (    A__      ):






 """simple docstring"""



 __lowercase							  = generate_pascal_triangle(A__      )
 for row_idx in range(A__      ):
  # Print left spaces
  for _ in range(num_rows - row_idx - 1      ):
   print(end=''' '''      )
  # Print row values
  for col_idx in range(row_idx + 1      ):
   if col_idx != row_idx:
    print(triangle[row_idx][col_idx]     ,				end=''' '''      )
   else:
    print(triangle[row_idx][col_idx]     ,				end=''''''      )
  print()


def 		_A     (    A__      ):






 """simple docstring"""



 if not isinstance(A__     ,				A__      ):
  raise TypeError('''The input value of \'num_rows\' should be \'int\''''      )

 if num_rows == 0:
  return []
 elif num_rows < 0:
  raise ValueError(
      '''The input value of \'num_rows\' should be greater than or equal to 0'''      )

 __lowercase							  = []
 for current_row_idx in range(A__      ):
  __lowercase							  = populate_current_row(A__     ,				A__      )
  triangle.append(A__      )
 return triangle


def 		_A     (    A__     ,				A__      ):






 """simple docstring"""



 __lowercase							  = [-1] * (current_row_idx + 1)
 # first and last elements of current row are equal to 1
 __lowercase  ,	__lowercase							  = 1, 1
 for current_col_idx in range(1     ,				A__      ):
  calculate_current_element(
      A__     ,				A__     ,				A__     ,				A__      )
 return current_row


def 		_A     (    A__     ,				A__     ,				A__     ,				A__     ,				):






 """simple docstring"""



 __lowercase							  = triangle[current_row_idx - 1][current_col_idx - 1]
 __lowercase							  = triangle[current_row_idx - 1][current_col_idx]
 __lowercase							  = above_to_left_elt + above_to_right_elt


def 		_A     (    A__      ):






 """simple docstring"""



 if not isinstance(A__     ,				A__      ):
  raise TypeError('''The input value of \'num_rows\' should be \'int\''''      )

 if num_rows == 0:
  return []
 elif num_rows < 0:
  raise ValueError(
      '''The input value of \'num_rows\' should be greater than or equal to 0'''      )

 __lowercase							  = [[1]]

 for row_index in range(1     ,				A__      ):
  __lowercase							  = [0] + result[-1] + [0]
  __lowercase							  = row_index + 1
  # Calculate the number of distinct elements in a row
  __lowercase							  = sum(divmod(A__     ,				2      )      )
  __lowercase							  = [
      temp_row[i - 1] + temp_row[i] for i in range(1     ,				distinct_elements + 1      )
  ]
  __lowercase							  = row_first_half[: (row_index + 1) // 2]
  row_second_half.reverse()
  __lowercase							  = row_first_half + row_second_half
  result.append(A__      )

 return result


def 		_A     (    ):






 """simple docstring"""



 from collections.abc import Callable
 from timeit import timeit

 def benchmark_a_function(A__     ,				A__      ) -> None:
  __lowercase							  = F"{func.__name__}({value})"
  __lowercase							  = timeit(F"__main__.{call}"     ,				setup='''import __main__'''      )
  # print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
  print(F"{call:38} -- {timing:.4f} seconds"      )

 for value in range(15      ):  # (1, 7, 14):
  for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
   benchmark_a_function(A__     ,				A__      )
  print()


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()





"""simple docstring"""



def   __lowerCAmelCase						(						)	->						Union[str, Any]:


    """simple docstring"""





    snake_case    :      Dict      					=    []
    snake_case    :      List[Any]      					=    1

    while len(lowercase ) < 1e6:
        constant.append(str(lowercase ) )
        i += 1

    snake_case    :      Tuple      					=    "".join(lowercase )

    return (
        int(constant[0] )
        * int(constant[9] )
        * int(constant[99] )
        * int(constant[999] )
        * int(constant[9999] )
        * int(constant[9_9999] )
        * int(constant[99_9999] )
    )


if __name__ == "__main__":
  print(solution())





