



import sys

__snake_case    :		Optional[int]  =(
    '73167176531330624919225119674426574742355349194934'
    '96983520312774506326239578318016984801869478851843'
    '85861560789112949495459501737958331952853208805511'
    '12540698747158523863050715693290963295227443043557'
    '66896648950445244523161731856403098711121722383113'
    '62229893423380308135336276614282806444486645238749'
    '30358907296290491560440772390713810515859307960866'
    '70172427121883998797908792274921901699720888093776'
    '65727333001053367881220235421809751254540594752243'
    '52584907711670556013604839586446706324415722155397'
    '53697817977846174064955149290862569321978468622482'
    '83972241375657056057490261407972968652414535100474'
    '82166370484403199890008895243450658541227588666881'
    '16427171479924442928230863465674813919123162824586'
    '17866458359124566529476545682848912883142607690042'
    '24219022671055626321111109370544217506941658960408'
    '07198403850962455444362981230987879927244284909188'
    '84580156166097919133875499200524063689912560717606'
    '05886116467109405077541002256983155200055935729725'
    '71636269561882670428252483600823257530420752963450'
)






def      lowerCAmelCase__		(   lowerCamelCase_		:		str = N):





				'''simple docstring'''

				lowerCAmelCase__					:    Dict												=					-sys.maxsize - 1
				for i in range(len(lowerCamelCase_) - 12):
								lowerCAmelCase__					:    Union[str, Any]												=					1
								for j in range(13):
												product *= int(n[i + j])
								if product > largest_product:
												lowerCAmelCase__					:    Union[str, Any]												=					product
				return largest_product


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










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






def      lowerCAmelCase__		(   lowerCamelCase_		:		ndarray):





				'''simple docstring'''

				return np.dot(lowerCamelCase_	,lowerCamelCase_)



class 	lowerCamelCase__      :




		'''simple docstring'''



		def __init__(self		,*,
		    __lowerCamelCase = np.inf		,__lowerCamelCase = "linear"		,__lowerCamelCase = 0.0		,)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    Any												=					regularization
						lowerCAmelCase__					:    str												=					gamma
						if kernel == "linear":
										lowerCAmelCase__					:    Dict												=					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'''			)
										lowerCAmelCase__					:    Optional[Any]												=					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:
										lowerCAmelCase__					:    List[str]												=					f"""Unknown kernel: {kernel}"""
										raise ValueError(__lowerCamelCase			)



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      float:

						"""simple docstring"""






						return np.dot(__lowerCamelCase		,__lowerCamelCase			)



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      float:

						"""simple docstring"""






						return np.exp(-(self.gamma * norm_squared(vectora - vectora			))			)



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    str												=					observations
						lowerCAmelCase__					:    Optional[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

						((lowerCAmelCase__)						,		)					:    List[str]												=					np.shape(__lowerCamelCase			)

						def to_minimize(__lowerCamelCase			) -> float:
										lowerCAmelCase__					:    List[str]												=					0
										((lowerCAmelCase__)						,		)					:    str												=					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			)

						lowerCAmelCase__					:    List[str]												=					LinearConstraint(__lowerCamelCase		,0		,0			)
						lowerCAmelCase__					:    List[str]												=					Bounds(0		,self.regularization			)

						lowerCAmelCase__					:    int												=					minimize(
						    __lowerCamelCase		,np.ones(__lowerCamelCase			)		,bounds=__lowerCamelCase		,constraints=[ly_contraint]			).x
						lowerCAmelCase__					:    List[Any]												=					l_star

						# calculating mean offset of separation plane to points
						lowerCAmelCase__					:    Optional[Any]												=					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]			)
						lowerCAmelCase__					:    Dict												=					s / n



		def 		lowerCAmelCase__				(self		,__lowerCamelCase			)					->      int:

						"""simple docstring"""






						lowerCAmelCase__					:    str												=					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()

