





def    __lowercase   (      _SCREAMING_SNAKE_CASE = 1_00_00_00	) ->   List[Any]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						limit + 1
      SCREAMING_SNAKE_CASE		=						[0] * limit
      for first_term in range(1 ,						A_	):
            for n in range(A_ ,						A_ ,						A_	):
                  SCREAMING_SNAKE_CASE		=						first_term + n / first_term
                  if common_difference % 4:  # d must be divisble by 4
                        continue
                  else:
                        common_difference /= 4
                        if (
                            first_term > common_difference
                            and first_term < 4 * common_difference
                        ):  # since x,y,z are positive integers
                              frequency[n] += 1  # so z>0 and a>d ,also 4d<a

      SCREAMING_SNAKE_CASE		=						sum(1 for x in frequency[1:limit] if x == 10	)

      return count


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





"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt

def   __SCREAMING_SNAKE_CASE  (      A_ = 1_00_00_00						,     A_ = 10 ):
	lowerCAmelCase__	:						defaultdict  				=	defaultdict(A_ )

	for outer_width in range(3						,     (t_limit // 4) + 2 ):
		if outer_width * outer_width > t_limit:
			lowerCAmelCase__	:						int  				=	max(
			    ceil(sqrt(outer_width * outer_width - t_limit ) )						,     1 )
		else:
			lowerCAmelCase__	:						Tuple  				=	1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(A_						,     outer_width - 1						,     2 ):
			count[outer_width * outer_width - hole_width * hole_width] += 1

	return sum(1 for n in count.values() if 1 <= n <= 10 )


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




