






"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt







def      lowerCamelCase__       (							_lowerCamelCase       :		int = 1000000		,				_lowerCamelCase       :		int = 10 )      ->				int:
  lowerCamelCase_         =						defaultdict(_lowerCamelCase )

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

    hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

    for hole_width in range(_lowerCamelCase		,				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() = }''')












"""simple docstring"""





from __future__ import annotations







def      lowerCamelCase__       (							_lowerCamelCase       :		int )      ->				list[int]:
  lowerCamelCase_         =						[True] * limit
  lowerCamelCase_         =						False
  lowerCamelCase_         =						False
  lowerCamelCase_         =						True

  for i in range(3		,				int(limit**0.5 + 1 )		,				2 ):
    lowerCamelCase_         =						i * 2
    while index < limit:
      lowerCamelCase_         =						False
      lowerCamelCase_         =						index + i

  lowerCamelCase_         =						[2]

  for i in range(3		,				_lowerCamelCase		,				2 ):
    if is_prime[i]:
      primes.append(_lowerCamelCase )

  return primes







def      lowerCamelCase__       (							_lowerCamelCase       :		int = 1000000 )      ->				int:
  lowerCamelCase_         =						prime_sieve(_lowerCamelCase )
  lowerCamelCase_         =						0
  lowerCamelCase_         =						0

  for i in range(len(_lowerCamelCase ) ):
    for j in range(i + length		,				len(_lowerCamelCase ) ):
      lowerCamelCase_         =						sum(primes[i:j] )
      if sol >= ceiling:
        break

      if sol in primes:
        lowerCamelCase_         =						j - i
        lowerCamelCase_         =						sol

  return largest


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




