




import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize







def        lowerCAmelCase_			(  snake_case_  ):
						return np.dot(snake_case_,snake_case_  )







class 		lowercase							:

					def __init__(						self	,  *,
					    _a = np.inf	,  _a = "linear"	,  _a = 0.0	,  )		->							None:
											_A							:  Tuple    =		regularization
											_A							:  str    =		gamma
											if kernel == "linear":
																	_A							:  str    =		self.__linear
											elif kernel == "rbf":
																	if self.gamma == 0:
																							raise ValueError("""rbf kernel requires gamma"""       )
																	if not isinstance(self.gamma	,  (float, int)       ):
																							raise ValueError("""gamma must be float or int"""       )
																	if not self.gamma > 0:
																							raise ValueError("""gamma must be > 0"""       )
																	_A							:  List[str]    =		self.__rbf
																	# in the future, there could be a default value like in sklearn
																	# sklear: def_gamma = 1/(n_features * X.var()) (wiki)
																	# previously it was 1/(n_features)
											else:
																	_A							:  Optional[Any]    =		F'''Unknown kernel: {kernel}'''
																	raise ValueError(_a       )

					def       a__			(						self	,  _a	,  _a       )		->							float:
											return np.dot(_a	,  _a       )

					def       a__			(						self	,  _a	,  _a       )		->							float:
											return np.exp(-(self.gamma * norm_squared(vectora - vectora       ))       )

					def       a__			(						self	,  _a	,  _a       )		->							None:
											_A							:  int    =		observations
											_A							:  int    =		classes

											# using Wolfe's Dual to calculate w.
											# Primal problem: minimize 1/2*norm_squared(w)
											#   constraint: yn(w . xn + b) >= 1
											#
											# With l a vector
											# Dual problem: maximize sum_n(ln) -
											#       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
											#   constraint: self.C >= ln >= 0
											#           and sum_n(ln*yn) = 0
											# Then we get w using w = sum_n(ln*yn*xn)
											# At the end we can get b ~= mean(yn - w . xn)
											#
											# Since we use kernels, we only need l_star to calculate b
											# and to classify observations

											(_A     )							:  Optional[int]    =		np.shape(_a       )

											def to_minimize(_a       ) -> float:
																	_A							:  Union[str, Any]    =		0
																	(_A     )							:  Optional[Any]    =		np.shape(_a       )
																	for i in range(_a       ):
																							for j in range(_a       ):
																													s += (
																													    candidate[i]
																													    * candidate[j]
																													    * classes[i]
																													    * classes[j]
																													    * self.kernel(observations[i]	,  observations[j]       )
																													)
																	return 1 / 2 * s - sum(_a       )

											_A							:  Any    =		LinearConstraint(_a	,  0	,  0       )
											_A							:  Optional[Any]    =		Bounds(0	,  self.regularization       )

											_A							:  Union[str, Any]    =		minimize(
											    _a	,  np.ones(_a       )	,  bounds=_a	,  constraints=[ly_contraint]       ).x
											_A							:  Dict    =		l_star

											# calculating mean offset of separation plane to points
											_A							:  Tuple    =		0
											for i in range(_a       ):
																	for j in range(_a       ):
																							s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
																							    observations[i]	,  observations[j]       )
											_A							:  List[str]    =		s / n



					def       a__			(						self	,  _a       )		->							int:
											_A							:  Union[str, Any]    =		sum(
											    self.optimum[n]
											    * self.classes[n]
											    * self.kernel(self.observations[n]	,  _a       )
											    for n in range(len(self.classes       )       )       )
											return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
		import doctest

		doctest.testmod()







def        lowerCAmelCase_			(  snake_case_ = 1000000  ):
      _A							:  Any    =		limit + 1
      _A							:  Tuple    =		[0] * limit
      for first_term in range(1,snake_case_  ):
            for n in range(snake_case_,snake_case_,snake_case_  ):
                  _A							:  Optional[int]    =		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

      _A							:  List[str]    =		sum(1 for x in frequency[1:limit] if x == 10  )

      return count


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

