






"""simple docstring"""


def  lowerCAmelCase    (   __UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase			):




  """simple docstring"""







  return len_board * len_board_column * row + column



def  lowerCAmelCase    (   __UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	):




  """simple docstring"""







  if board[row][column] != word[word_index]:
    return False

  if word_index == len(__UpperCamelCase			) - 1:
    return True

  __A						      =			[(0, 1), (0, -1), (-1, 0), (1, 0)]
  __A						      =			len(__UpperCamelCase			)
  __A						      =			len(board[0]			)
  for direction in traverts_directions:
    __A						      =			row + direction[0]
    __A						      =			column + direction[1]
    if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
      continue

    __A						      =			get_point_key(__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase			)
    if key in visited_points_set:
      continue

    visited_points_set.add(__UpperCamelCase			)
    if exits_word(__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	word_index + 1		,	__UpperCamelCase			):
      return True

    visited_points_set.remove(__UpperCamelCase			)

  return False



def  lowerCAmelCase    (   __UpperCamelCase		,	__UpperCamelCase			):




  """simple docstring"""







  __A						      =			(
      '''The board should be a non empty matrix of single chars strings.'''
  )

  __A						      =			len(__UpperCamelCase			)
  if not isinstance(__UpperCamelCase		,	__UpperCamelCase			) or len(__UpperCamelCase			) == 0:
    raise ValueError(__UpperCamelCase			)

  for row in board:
    if not isinstance(__UpperCamelCase		,	__UpperCamelCase			) or len(__UpperCamelCase			) == 0:
      raise ValueError(__UpperCamelCase			)

    for item in row:
      if not isinstance(__UpperCamelCase		,	__UpperCamelCase			) or len(__UpperCamelCase			) != 1:
        raise ValueError(__UpperCamelCase			)

    # Validate word
  if not isinstance(__UpperCamelCase		,	__UpperCamelCase			) or len(__UpperCamelCase			) == 0:
    raise ValueError(
        '''The word parameter should be a string of length greater than 0.'''			)

  __A						      =			len(board[0]			)
  for i in range(__UpperCamelCase			):
    for j in range(__UpperCamelCase			):
      if exits_word(
          __UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	0		,	{get_point_key(__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase		,	__UpperCamelCase			)}			):
        return True

  return False


if __name__ == "__main__":
       import doctest

       doctest.testmod()












"""simple docstring"""


from itertools import product



def  lowerCAmelCase    (   __UpperCamelCase = 1_5			):




  """simple docstring"""







  __A						      =			0.0
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42

  for series in product(range(2			)		,	repeat=__UpperCamelCase			):
    __A						      =			series.count(1			)
    __A						      =			num_turns - num_blue
    if num_red >= num_blue:
      continue
    __A						      =			1.0
    for ind, col in enumerate(__UpperCamelCase		,	2			):
      if col == 0:
        prob *= (ind - 1) / ind
      else:
        prob *= 1 / ind

    total_prob += prob

  return int(1 / total_prob			)


if __name__ == "__main__":
       print(F'''{solution() = }''')




