import math


def 							lowerCAmelCase__    (       a__      )	->bool:




  '''simple docstring'''

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5  ,			int(math.sqrt(a__      ) + 1      )  ,			6      ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True


def 							lowerCAmelCase__    (       a__ = 600_851_475_143      )	->int:




  '''simple docstring'''

  try:
    _UpperCamelCase				=  int(a__      )
  except (TypeError, ValueError):
    raise TypeError("Parameter n must be int or castable to int."      )
  if n <= 0:
    raise ValueError("Parameter n must be greater than or equal to one."      )
  _UpperCamelCase				=  0
  if is_prime(a__      ):
    return n
  while n % 2 == 0:
    n //= 2
  if is_prime(a__      ):
    return n
  for i in range(3  ,			int(math.sqrt(a__      )      ) + 1  ,			2      ):
    if n % i == 0:
      if is_prime(n // i      ):
        _UpperCamelCase				=  n // i
        break
      elif is_prime(a__      ):
        _UpperCamelCase				=  i
  return max_number


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





from itertools import combinations, product


def 							lowerCAmelCase__    (       a__  ,			a__  ,			a__  ,			a__      )	->bool:




  '''simple docstring'''

  if xa == ya == 0 or xa == ya == 0:
    return False
  _UpperCamelCase				=  xa * xa + ya * ya
  _UpperCamelCase				=  xa * xa + ya * ya
  _UpperCamelCase				=  (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
  return (
      a_square + b_square == c_square
      or a_square + c_square == b_square
      or b_square + c_square == a_square
  )


def 							lowerCAmelCase__    (       a__ = 50      )	->int:




  '''simple docstring'''

  return sum(
      1
      for pta, pta in combinations(product(range(limit + 1      )  ,			repeat=2      )  ,			2      )
      if is_right(*a__  ,			*a__      )      )


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




