"""simple docstring"""





from math import log

from scipy.constants import Boltzmann, physical_constants

__A     = 300  # TEMPERATURE (unit = K)


def       lowercase_      (      _lowerCamelCase:		Any  ,      _lowerCamelCase:		Dict  ,      _lowerCamelCase:		Dict  ,      )       ->					float:



							'''simple docstring'''

							if donor_conc <= 0:
														raise ValueError("Donor concentration should be positive"					)
							elif acceptor_conc <= 0:
														raise ValueError("Acceptor concentration should be positive"					)
							elif intrinsic_conc <= 0:
														raise ValueError("Intrinsic concentration should be positive"					)
							elif donor_conc <= intrinsic_conc:
														raise ValueError(
														    "Donor concentration should be greater than intrinsic concentration"					)
							elif acceptor_conc <= intrinsic_conc:
														raise ValueError(
														    "Acceptor concentration should be greater than intrinsic concentration"					)
							else:
														return (
														    Boltzmann
														    * T
														    * log((donor_conc * acceptor_conc) / intrinsic_conc**2					)
														    / physical_constants["electron volt"][0]
														)


if __name__ == "__main__":
				import doctest

				doctest.testmod()






"""simple docstring"""





import math
def  __A   (_SCREAMING_SNAKE_CASE			)					->int:





  """simple docstring"""


  if not isinstance(_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE			):
    lowerCAmelCase__			:Dict											=							F"Input value of [number={number}] must be an integer"
    raise TypeError(_SCREAMING_SNAKE_CASE			)

  if number < 1:
    lowerCAmelCase__			:Dict											=							F"Input value of [number={number}] must be > 0"
    raise ValueError(_SCREAMING_SNAKE_CASE			)
  elif number == 1:
    return 3
  elif number == 2:
    return 5
  else:
    lowerCAmelCase__			:Union[str, Any]											=							int(math.log(number // 3     ,   2			)			) + 2

    lowerCAmelCase__			:Optional[Any]											=							[3, 5]
    lowerCAmelCase__			:Optional[Any]											=							2
    lowerCAmelCase__			:List[str]											=							3
    for block in range(1     ,   _SCREAMING_SNAKE_CASE			):
      for _ in range(_SCREAMING_SNAKE_CASE			):
        proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]			)
        proth_index += 1
      increment *= 2

  return proth_list[number - 1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  for number in range(11):
    __A											=		0
    try:
      __A											=		proth(number)
    except ValueError:
      print(F'''ValueError: there is no {number}th Proth number''')
      continue

    print(F'''The {number}th Proth number: {value}''')
