




import math
from decimal import Decimal, getcontext




def        __SCREAMING_SNAKE_CASE (	lowercase_ = 4_00_00_00   )							->						int:

    """simple docstring"""


    try:
        __UpperCamelCase			=    int(lowercase_   )
    except (TypeError, ValueError):
        raise TypeError('''Parameter n must be int or castable to int.'''   )
    if n <= 0:
        raise ValueError('''Parameter n must be greater than or equal to one.'''   )
    __UpperCamelCase			=    1_00
    __UpperCamelCase			=    (Decimal(5   ) ** Decimal(0.5   ) + 1) / Decimal(2   )

    __UpperCamelCase			=    (math.floor(math.log(n * (phi + 2)       ,  lowercase_   ) - 1   ) // 3) * 3 + 2
    __UpperCamelCase			=    Decimal(round(phi ** Decimal(index + 1   )   )   ) / (phi + 2)
    __UpperCamelCase			=    num // 2
    return int(lowercase_   )


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










from __future__ import annotations
def 							UpperCAmelCase_   (				__snake_case		)	->     list[int]:







 """simple docstring"""


 if not list_of_ints:
  return []

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

 _lowercase				 =max(len(bin(__snake_case		)[2:]		) for x in list_of_ints		)
 return _msd_radix_sort(__snake_case	,		__snake_case		)
def 							UpperCAmelCase_   (				__snake_case	,		__snake_case		)	->     list[int]:







 """simple docstring"""


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

 _lowercase				 =[]
 _lowercase				 =[]
 # 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(__snake_case		)
  else:
   # number has a zero at bit bit_position
   zeros.append(__snake_case		)

    # recursively split both lists further
 _lowercase				 =_msd_radix_sort(__snake_case	,		bit_position - 1		)
 _lowercase				 =_msd_radix_sort(__snake_case	,		bit_position - 1		)

 # recombine lists
 _lowercase				 =zeros
 res.extend(__snake_case		)

 return res
def 							UpperCAmelCase_   (				__snake_case		)	->     List[str]:







 """simple docstring"""


 _lowercase				 =len(__snake_case		)
 if not list_of_ints or length == 1:
  return

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

 _lowercase				 =max(len(bin(__snake_case		)[2:]		) for x in list_of_ints		)
 _msd_radix_sort_inplace(__snake_case	,		__snake_case	,		0	,		__snake_case		)
def 							UpperCAmelCase_   (				__snake_case	,		__snake_case	,		__snake_case	,		__snake_case		)	->     Any:







 """simple docstring"""


 if bit_position == 0 or end_index - begin_index <= 1:
  return

 bit_position -= 1

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

  if changed:
   continue

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

 _msd_radix_sort_inplace(__snake_case	,		__snake_case	,		__snake_case	,		__snake_case		)
 _msd_radix_sort_inplace(__snake_case	,		__snake_case	,		__snake_case	,		__snake_case		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

