
from __future__ import annotations





def    _a (						lowerCamelCase							):
 if not list_of_ints:
  return []

 if min(lowerCamelCase							) < 0:
  raise ValueError("""All numbers must be positive"""							)

 lowerCamelCase		:     str          =				max(len(bin(lowerCamelCase							)[2:]							) for x in list_of_ints							)
 return _msd_radix_sort(lowerCamelCase,     lowerCamelCase							)





def    _a (						lowerCamelCase,     lowerCamelCase							):
 if bit_position == 0 or len(lowerCamelCase							) in [0, 1]:
  return list_of_ints

 lowerCamelCase		:     Dict          =				[]
 lowerCamelCase		:     Tuple          =				[]
 # Split numbers based on bit at bit_position from the right
 for number in list_of_ints:
  if (number >> (bit_position - 1)) & 1:
   # number has a one at bit bit_position
   ones.append(lowerCamelCase							)
  else:
   # number has a zero at bit bit_position
   zeros.append(lowerCamelCase							)

    # recursively split both lists further
 lowerCamelCase		:     int          =				_msd_radix_sort(lowerCamelCase,     bit_position - 1							)
 lowerCamelCase		:     Optional[Any]          =				_msd_radix_sort(lowerCamelCase,     bit_position - 1							)

 # recombine lists
 lowerCamelCase		:     List[str]          =				zeros
 res.extend(lowerCamelCase							)

 return res





def    _a (						lowerCamelCase							):
 lowerCamelCase		:     Dict          =				len(lowerCamelCase							)
 if not list_of_ints or length == 1:
  return

 if min(lowerCamelCase							) < 0:
  raise ValueError("""All numbers must be positive"""							)

 lowerCamelCase		:     Any          =				max(len(bin(lowerCamelCase							)[2:]							) for x in list_of_ints							)
 _msd_radix_sort_inplace(lowerCamelCase,     lowerCamelCase,     0,     lowerCamelCase							)





def    _a (						lowerCamelCase,     lowerCamelCase,     lowerCamelCase,     lowerCamelCase							):
 if bit_position == 0 or end_index - begin_index <= 1:
  return

 bit_position -= 1

 lowerCamelCase		:     int          =				begin_index
 lowerCamelCase		:     Tuple          =				end_index - 1
 while i <= j:
  lowerCamelCase		:     Dict          =				False
  if not (list_of_ints[i] >> bit_position) & 1:
   # found zero at the beginning
   i += 1
   lowerCamelCase		:     Optional[Any]          =				True
  if (list_of_ints[j] >> bit_position) & 1:
   # found one at the end
   j -= 1
   lowerCamelCase		:     List[str]          =				True

  if changed:
   continue

  lowerCamelCase      ,   lowerCamelCase		:     Union[str, Any]          =				list_of_ints[j], list_of_ints[i]
  j -= 1
  if j != i:
   i += 1

 _msd_radix_sort_inplace(lowerCamelCase,     lowerCamelCase,     lowerCamelCase,     lowerCamelCase							)
 _msd_radix_sort_inplace(lowerCamelCase,     lowerCamelCase,     lowerCamelCase,     lowerCamelCase							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()






def    _a (						lowerCamelCase,     lowerCamelCase,     lowerCamelCase							):
 lowerCamelCase		:     Optional[int]          =				[1 / first_term]
 lowerCamelCase		:     Any          =				1 / first_term
 for _ in range(number_of_terms - 1							):
  first_term += common_difference
  arithmetic_progression.append(lowerCamelCase							)
 lowerCamelCase		:     Optional[Any]          =				[1 / step for step in arithmetic_progression]
 return sum(lowerCamelCase							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      print(sum_of_harmonic_progression(1 / 2, 2, 2))




