






"""simple docstring"""





def      lowerCamelCase__       (							_lowerCamelCase       :		list[int]		,				_lowerCamelCase       :		list[int]		,				_lowerCamelCase       :		int )      ->				bool:
  return not any(
      neighbour == 1 and colored_vertices[i] == color
      for i, neighbour in enumerate(_lowerCamelCase ) )







def      lowerCamelCase__       (							_lowerCamelCase       :		list[list[int]]		,				_lowerCamelCase       :		int		,				_lowerCamelCase       :		list[int]		,				_lowerCamelCase       :		int )      ->				bool:

  # Base Case
  if index == len(_lowerCamelCase ):
    return True

  # Recursive Step
  for i in range(_lowerCamelCase ):
    if valid_coloring(graph[index]		,				_lowerCamelCase		,				_lowerCamelCase ):
      # Color current vertex
      lowerCamelCase_         =						i
      # Validate coloring
      if util_color(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase		,				index + 1 ):
        return True
      # Backtrack
      lowerCamelCase_         =						-1
  return False







def      lowerCamelCase__       (							_lowerCamelCase       :		list[list[int]]		,				_lowerCamelCase       :		int )      ->				list[int]:
  lowerCamelCase_         =						[-1] * len(_lowerCamelCase )

  if util_color(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase		,				0 ):
    return colored_vertices

  return []












"""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() = }''')




