






"""simple docstring"""


from __future__ import annotations




def 					a			(  UpperCamelCase_				:					list[int]		)	->		list[int]:
 if not list_of_ints:
  return []

 if min(UpperCamelCase_		) < 0:
  raise ValueError('All numbers must be positive'		)

 __A						:							Optional[int]      =						max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
 return _msd_radix_sort(UpperCamelCase_  ,						UpperCamelCase_		)




def 					a			(  UpperCamelCase_				:					list[int]  ,						UpperCamelCase_				:					int		)	->		list[int]:
 if bit_position == 0 or len(UpperCamelCase_		) in [0, 1]:
  return list_of_ints

 __A						:							List[str]      =						[]
 __A						:							Union[str, Any]      =						[]
 # 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(UpperCamelCase_		)
  else:
   # number has a zero at bit bit_position
   zeros.append(UpperCamelCase_		)

    # recursively split both lists further
 __A						:							Any      =						_msd_radix_sort(UpperCamelCase_  ,						bit_position - 1		)
 __A						:							Any      =						_msd_radix_sort(UpperCamelCase_  ,						bit_position - 1		)

 # recombine lists
 __A						:							Tuple      =						zeros
 res.extend(UpperCamelCase_		)

 return res




def 					a			(  UpperCamelCase_				:					list[int]		)	->		Optional[int]:
 __A						:							Any      =						len(UpperCamelCase_		)
 if not list_of_ints or length == 1:
  return

 if min(UpperCamelCase_		) < 0:
  raise ValueError('All numbers must be positive'		)

 __A						:							Union[str, Any]      =						max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
 _msd_radix_sort_inplace(UpperCamelCase_  ,						UpperCamelCase_  ,						0  ,						UpperCamelCase_		)




def 					a			(  UpperCamelCase_				:					list[int]  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int		)	->		Any:
 if bit_position == 0 or end_index - begin_index <= 1:
  return

 bit_position -= 1

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

  if changed:
   continue

  __A     ,       __A						:							int      =						list_of_ints[j], list_of_ints[i]
  j -= 1
  if j != i:
   i += 1

 _msd_radix_sort_inplace(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)
 _msd_radix_sort_inplace(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()













"""simple docstring"""


import math




def 					a			(  UpperCamelCase_				:					int		)	->		str:
 if number == 0:
  __A						:							Dict      =						'Zero'
  return words
 else:
  __A						:							List[str]      =						math.logaa(UpperCamelCase_		)
  __A						:							Union[str, Any]      =						digits + 1
  __A						:							List[str]      =						{}
  __A						:							int      =						''
  __A						:							Any      =						'One'
  __A						:							Tuple      =						'Two'
  __A						:							Any      =						'Three'
  __A						:							Any      =						'Four'
  __A						:							Optional[Any]      =						'Five'
  __A						:							List[Any]      =						'Six'
  __A						:							List[Any]      =						'Seven'
  __A						:							Dict      =						'Eight'
  __A						:							Union[str, Any]      =						'Nine'

  __A						:							List[Any]      =						{}
  __A						:							Tuple      =						''
  __A						:							List[Any]      =						'Twenty'
  __A						:							Optional[Any]      =						'Thirty'
  __A						:							Any      =						'Forty'
  __A						:							Optional[int]      =						'Fifty'
  __A						:							Dict      =						'Sixty'
  __A						:							Dict      =						'Seventy'
  __A						:							Optional[Any]      =						'Eighty'
  __A						:							Any      =						'Ninety'

  __A						:							int      =						{}
  __A						:							List[str]      =						'Ten'
  __A						:							Optional[Any]      =						'Eleven'
  __A						:							Dict      =						'Twelve'
  __A						:							Union[str, Any]      =						'Thirteen'
  __A						:							Union[str, Any]      =						'Fourteen'
  __A						:							Dict      =						'Fifteen'
  __A						:							str      =						'Sixteen'
  __A						:							str      =						'Seventeen'
  __A						:							Union[str, Any]      =						'Eighteen'
  __A						:							Union[str, Any]      =						'Nineteen'

  __A						:							Optional[Any]      =						{}
  __A						:							Optional[int]      =						'Hundred,'
  __A						:							Union[str, Any]      =						'Thousand,'
  __A						:							Union[str, Any]      =						'Lakh,'
  __A						:							Union[str, Any]      =						'Crore,'

  __A						:							Optional[Any]      =						number
  __A						:							Optional[Any]      =						''
  __A						:							List[str]      =						0
  __A						:							List[str]      =						int(UpperCamelCase_		)
  while counter < digits:
   __A						:							Any      =						temp_num % 1_0
   if counter % 2 == 0:
    __A						:							Optional[Any]      =						''
    if counter in placevalue and current != 0:
     __A						:							Union[str, Any]      =						placevalue[counter]
    if counter == 2:
     __A						:							Dict      =						singles[current] + addition + words
    elif counter == 0:
     if ((temp_num % 1_0_0) // 1_0) == 1:
      __A						:							Any      =						teens[current] + addition + words
      __A						:							int      =						temp_num // 1_0
      counter += 1
     else:
      __A						:							Optional[Any]      =						singles[current] + addition + words

    else:
     __A						:							str      =						doubles[current] + addition + words

   else:
    if counter == 1:
     if current == 1:
      __A						:							List[Any]      =						teens[number % 1_0] + words
     else:
      __A						:							Union[str, Any]      =						''
      if counter in placevalue:
       __A						:							int      =						placevalue[counter]
      __A						:							Optional[Any]      =						doubles[current] + addition + words
    else:
     __A						:							Any      =						''
     if counter in placevalue:
      if current == 0 and ((temp_num % 1_0_0) // 1_0) == 0:
       __A						:							Optional[int]      =						''
      else:
       __A						:							Optional[int]      =						placevalue[counter]
     if ((temp_num % 1_0_0) // 1_0) == 1:
      __A						:							Dict      =						teens[current] + addition + words
      __A						:							Any      =						temp_num // 1_0
      counter += 1
     else:
      __A						:							List[str]      =						singles[current] + addition + words
   counter += 1
   __A						:							Dict      =						temp_num // 1_0
 return words


if __name__ == "__main__":
   import doctest

   doctest.testmod()





