"""simple docstring"""
from __future__ import annotations







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->list[tuple[int, int]]:
  a__							,    a__:     Union[str, Any]										=	position
  a__:     int										=	[
      (y + 1, x + 2),
      (y - 1, x + 2),
      (y + 1, x - 2),
      (y - 1, x - 2),
      (y + 2, x + 1),
      (y + 2, x - 1),
      (y - 2, x + 1),
      (y - 2, x - 1),
  ]
  a__:     Any										=	[]

  for position in positions:
    a__							,    a__:     List[str]										=	position
    if 0 <= y_test < n and 0 <= x_test < n:
      permissible_positions.append(_SCREAMING_SNAKE_CASE   )

  return permissible_positions







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->bool:
  return not any(elem == 0 for row in board for elem in row   )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->bool:

  if is_complete(_SCREAMING_SNAKE_CASE   ):
    return True

  for position in get_valid_pos(_SCREAMING_SNAKE_CASE		,     len(_SCREAMING_SNAKE_CASE   )   ):
    a__							,    a__:     Tuple										=	position

    if board[y][x] == 0:
      a__:     Dict										=	curr + 1
      if open_knight_tour_helper(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     curr + 1   ):
        return True
      a__:     Tuple										=	0

  return False







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->list[list[int]]:
  a__:     Union[str, Any]										=	[[0 for i in range(_SCREAMING_SNAKE_CASE   )] for j in range(_SCREAMING_SNAKE_CASE   )]

  for i in range(_SCREAMING_SNAKE_CASE   ):
    for j in range(_SCREAMING_SNAKE_CASE   ):
      a__:     List[str]										=	1
      if open_knight_tour_helper(_SCREAMING_SNAKE_CASE		,     (i, j)		,     1   ):
        return board
      a__:     Optional[int]										=	0

  a__:     Tuple										=	F'Open Kight Tour cannot be performed on a board of size {n}'
  raise ValueError(_SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()



"""simple docstring"""
from math import pow, sqrt







def 						__a   (	*_SCREAMING_SNAKE_CASE   )	->bool:
  a__:     Union[str, Any]										=	len(_SCREAMING_SNAKE_CASE   ) > 0 and all(value > 0.0 for value in values   )
  return result







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError('Input Error: Molar mass values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,     2   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,     2   ) / molar_mass		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )


