





import math
import sys


def _A       (   __magic_name__	):
   if number != int(__magic_name__	):
      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
   lowercase__			       =  [-1] * (number + 1)
   lowercase__			       =  0
   for i in range(1  , number + 1	):
      lowercase__			       =  sys.maxsize
      lowercase__			       =  int(math.sqrt(__magic_name__	)	)
      for j in range(1  , root + 1	):
         lowercase__			       =  1 + answers[i - (j**2)]
         lowercase__			       =  min(__magic_name__  , __magic_name__	)
      lowercase__			       =  answer
   return answers[number]


if __name__ == "__main__":
  import doctest

  doctest.testmod()













import math


def _A       (   __magic_name__	):
   lowercase__			       =  math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

   return exponent == int(__magic_name__	)


def _A       (   __magic_name__ = 1 / 1_2345	):
   lowercase__			       =  0
   lowercase__			       =  0

   lowercase__			       =  3
   while True:
      lowercase__			       =  (integer**2 - 1) / 4
      # if candidate is an integer, then there is a partition for k
      if partition_candidate == int(__magic_name__	):
         lowercase__			       =  int(__magic_name__	)
         total_partitions += 1
         if check_partition_perfect(__magic_name__	):
            perfect_partitions += 1
      if perfect_partitions > 0:
         if perfect_partitions / total_partitions < max_proportion:
            return int(__magic_name__	)
      integer += 1


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






