import math
import sys


def     __lowerCAmelCase						(       a_		)      ->	int:





     '''simple docstring'''





     if number != int(a_		):
          raise ValueError('the value of input must be a natural number'		)
     if number < 0:
          raise ValueError('the value of input must not be a negative number'		)
     if number == 0:
          return 1
     SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       [-1] * (number + 1)
     SCREAMING_SNAKE_CASE					:			List[str]    	=       0
     for i in range(1       ,      number + 1		):
          SCREAMING_SNAKE_CASE					:			List[Any]    	=       sys.maxsize
          SCREAMING_SNAKE_CASE					:			int    	=       int(math.sqrt(a_		)		)
          for j in range(1       ,      root + 1		):
               SCREAMING_SNAKE_CASE					:			List[str]    	=       1 + answers[i - (j**2)]
               SCREAMING_SNAKE_CASE					:			List[str]    	=       min(a_       ,      a_		)
          SCREAMING_SNAKE_CASE					:			str    	=       answer
     return answers[number]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




'''simple docstring'''





def     __lowerCAmelCase						(       a_       ,      a_		)      ->	str:





     '''simple docstring'''





     if number < 0 or shift_amount < 0:
          raise ValueError('both inputs must be positive integers'		)

     SCREAMING_SNAKE_CASE					:			str    	=       str(bin(a_		)		)
     binary_number += "0" * shift_amount
     return binary_number


def     __lowerCAmelCase						(       a_       ,      a_		)      ->	str:





     '''simple docstring'''





     if number < 0 or shift_amount < 0:
          raise ValueError('both inputs must be positive integers'		)

     SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       str(bin(a_		)		)[2:]
     if shift_amount >= len(a_		):
          return "0b0"
     SCREAMING_SNAKE_CASE					:			Dict    	=       binary_number[: len(a_		) - shift_amount]
     return "0b" + shifted_binary_number


def     __lowerCAmelCase						(       a_       ,      a_		)      ->	str:





     '''simple docstring'''





     if number >= 0:  # Get binary representation of positive number
          SCREAMING_SNAKE_CASE					:			Tuple    	=       '0' + str(bin(a_		)		).strip('-'		)[2:]
     else:  # Get binary (2's complement) representation of negative number
          SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       len(bin(a_		)[3:]		)  # Find 2's complement of number
          SCREAMING_SNAKE_CASE					:			Any    	=       bin(abs(a_		) - (1 << binary_number_length)		)[3:]
          SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       (
              '1' + '0' * (binary_number_length - len(a_		)) + binary_number
          )

     if shift_amount >= len(a_		):
          return "0b" + binary_number[0] * len(a_		)
     return (
         "0b"
         + binary_number[0] * shift_amount
         + binary_number[: len(a_		) - shift_amount]
     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()



