"""simple docstring"""






from __future__ import annotations

import typing
from collections import Counter



def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__             =							Counter()
				for base in range(1					,			max_perimeter + 1       ):
								for perpendicular in range(lowerCamelCase					,			max_perimeter + 1       ):
												UpperCAmelCase__             =							(base * base + perpendicular * perpendicular) ** 0.5
												if hypotenuse == int(lowerCamelCase       ):
																UpperCAmelCase__             =							int(base + perpendicular + hypotenuse       )
																if perimeter > max_perimeter:
																				continue
																triplets[perimeter] += 1
				return triplets



def   a_						(					lowerCamelCase = 1_0_0_0       ):
				UpperCAmelCase__             =							pythagorean_triple(lowerCamelCase       )
				return triplets.most_common(1       )[0][0]


if __name__ == "__main__":
						print(F"""Perimeter {solution()} has maximum solutions""")




"""simple docstring"""






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



def   a_						(					lowerCamelCase       ):
				return np.dot(lowerCamelCase					,			lowerCamelCase       )
class 				snake_case       :




					"""simple docstring"""

					def __init__(				self   :	int    ,*,
					    lowerCamelCase__   :	float = np.inf    ,lowerCamelCase__   :	str = "linear"    ,lowerCamelCase__   :	float = 0.0    ,):
									UpperCAmelCase__             =							regularization
									UpperCAmelCase__             =							gamma
									if kernel == "linear":
													UpperCAmelCase__             =							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'			)
													UpperCAmelCase__             =							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:
													UpperCAmelCase__             =							f'''Unknown kernel: {kernel}'''
													raise ValueError(lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	List[Any]    ,lowerCamelCase__   :	ndarray    ,lowerCamelCase__   :	ndarray			):
									return np.dot(lowerCamelCase__    ,lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Any    ,lowerCamelCase__   :	ndarray    ,lowerCamelCase__   :	ndarray			):
									return np.exp(-(self.gamma * norm_squared(vectora - vectora			))			)







					def 		__lowerCAmelCase						(				self   :	Tuple    ,lowerCamelCase__   :	list[ndarray]    ,lowerCamelCase__   :	ndarray			):
									UpperCAmelCase__             =							observations
									UpperCAmelCase__             =							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

									((UpperCAmelCase__)      ,	)             =							np.shape(lowerCamelCase__			)

									def to_minimize(lowerCamelCase__   :	ndarray			) -> float:
													UpperCAmelCase__             =							0
													((UpperCAmelCase__)      ,	)             =							np.shape(lowerCamelCase__			)
													for i in range(lowerCamelCase__			):
																	for j in range(lowerCamelCase__			):
																					s += (
																					    candidate[i]
																					    * candidate[j]
																					    * classes[i]
																					    * classes[j]
																					    * self.kernel(observations[i]    ,observations[j]			)
																					)
													return 1 / 2 * s - sum(lowerCamelCase__			)

									UpperCAmelCase__             =							LinearConstraint(lowerCamelCase__    ,0    ,0			)
									UpperCAmelCase__             =							Bounds(0    ,self.regularization			)

									UpperCAmelCase__             =							minimize(
									    lowerCamelCase__    ,np.ones(lowerCamelCase__			)    ,bounds=lowerCamelCase__    ,constraints=[ly_contraint]			).x
									UpperCAmelCase__             =							l_star

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







					def 		__lowerCAmelCase						(				self   :	int    ,lowerCamelCase__   :	ndarray			):
									UpperCAmelCase__             =							sum(
									    self.optimum[n]
									    * self.classes[n]
									    * self.kernel(self.observations[n]    ,lowerCamelCase__			)
									    for n in range(len(self.classes			)			)			)
									return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()



