
"""simple docstring"""





import sys

_a														=		(
    '''73167176531330624919225119674426574742355349194934'''
    '''96983520312774506326239578318016984801869478851843'''
    '''85861560789112949495459501737958331952853208805511'''
    '''12540698747158523863050715693290963295227443043557'''
    '''66896648950445244523161731856403098711121722383113'''
    '''62229893423380308135336276614282806444486645238749'''
    '''30358907296290491560440772390713810515859307960866'''
    '''70172427121883998797908792274921901699720888093776'''
    '''65727333001053367881220235421809751254540594752243'''
    '''52584907711670556013604839586446706324415722155397'''
    '''53697817977846174064955149290862569321978468622482'''
    '''83972241375657056057490261407972968652414535100474'''
    '''82166370484403199890008895243450658541227588666881'''
    '''16427171479924442928230863465674813919123162824586'''
    '''17866458359124566529476545682848912883142607690042'''
    '''24219022671055626321111109370544217506941658960408'''
    '''07198403850962455444362981230987879927244284909188'''
    '''84580156166097919133875499200524063689912560717606'''
    '''05886116467109405077541002256983155200055935729725'''
    '''71636269561882670428252483600823257530420752963450'''
)



def       lowerCamelCase__		(			__snake_case = N	)							->		int:


					"""simple docstring"""





					_UpperCamelCase							 =  -sys.maxsize - 1
					for i in range(len(_snake_case	) - 12	):
										_UpperCamelCase							 =  1
										for j in range(13	):
															product *= int(n[i + j]	)
										if product > largest_product:
															_UpperCamelCase							 =  product
					return largest_product


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










"""simple docstring"""





import mpmath  # for roots of unity
import numpy as np



class 						snake_case_:






     def __init__(		self     :    str    , UpperCamelCase_     :    int=None    , UpperCamelCase_     :    List[str]=None ):
           # Input as list
           lowerCAmelCase    :		str				=      list(poly_a or [0] )[:]
           lowerCAmelCase    :		Any				=      list(poly_b or [0] )[:]

           # Remove leading zero coefficients
           while self.polyA[-1] == 0:
                 self.polyA.pop()
           lowerCAmelCase    :		Optional[int]				=      len(self.polyA )

           while self.polyB[-1] == 0:
                 self.polyB.pop()
           lowerCAmelCase    :		Union[str, Any]				=      len(self.polyB )

           # Add 0 to make lengths equal a power of 2
           lowerCAmelCase    :		str				=      int(
               2 ** np.ceil(np.loga(len(self.polyA ) + len(self.polyB ) - 1 ) ) )

           while len(self.polyA ) < self.c_max_length:
                 self.polyA.append(0 )
           while len(self.polyB ) < self.c_max_length:
                 self.polyB.append(0 )
           # A complex root used for the fourier transform
           lowerCAmelCase    :		int				=      complex(mpmath.root(x=1    , n=self.c_max_length    , k=1 ) )

           # The product
           lowerCAmelCase    :		int				=      self.__multiply()






     def    lowerCamelCase__   (		self     :    List[str]    , UpperCamelCase_     :    str ):
           lowerCAmelCase    :		Optional[Any]				=      [[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
           # Corner case
           if len(UpperCamelCase_ ) <= 1:
                 return dft[0]
           #
           lowerCAmelCase    :		Tuple				=      self.c_max_length // 2
           while next_ncol > 0:
                 lowerCAmelCase    :		Dict				=      [[] for i in range(UpperCamelCase_ )]
                 lowerCAmelCase    :		List[Any]				=      self.root**next_ncol

                 # First half of next step
                 lowerCAmelCase    :		Dict				=      1
                 for j in range(self.c_max_length // (next_ncol * 2) ):
                       for i in range(UpperCamelCase_ ):
                             new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j] )
                       current_root *= root
                 # Second half of next step
                 lowerCAmelCase    :		int				=      1
                 for j in range(self.c_max_length // (next_ncol * 2) ):
                       for i in range(UpperCamelCase_ ):
                             new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j] )
                       current_root *= root
                 # Update
                 lowerCAmelCase    :		Optional[Any]				=      new_dft
                 lowerCAmelCase    :		Union[str, Any]				=      next_ncol // 2
           return dft[0]






     def    lowerCamelCase__   (		self     :    List[Any] ):
           lowerCAmelCase    :		Optional[Any]				=      self.__dft('''A''' )
           lowerCAmelCase    :		Optional[int]				=      self.__dft('''B''' )
           lowerCAmelCase    :		Any				=      [[dft_a[i] * dft_b[i] for i in range(self.c_max_length )]]
           del dft_a
           del dft_b

           # Corner Case
           if len(inverce_c[0] ) <= 1:
                 return inverce_c[0]
           # Inverse DFT
           lowerCAmelCase    :		str				=      2
           while next_ncol <= self.c_max_length:
                 lowerCAmelCase    :		Union[str, Any]				=      [[] for i in range(UpperCamelCase_ )]
                 lowerCAmelCase    :		Optional[Any]				=      self.root ** (next_ncol // 2)
                 lowerCAmelCase    :		Tuple				=      1
                 # First half of next step
                 for j in range(self.c_max_length // next_ncol ):
                       for i in range(next_ncol // 2 ):
                             # Even positions
                             new_inverse_c[i].append(
                                 (
                                     inverce_c[i][j]
                                     + inverce_c[i][j + self.c_max_length // next_ncol]
                                 )
                                 / 2 )
                             # Odd positions
                             new_inverse_c[i + next_ncol // 2].append(
                                 (
                                     inverce_c[i][j]
                                     - inverce_c[i][j + self.c_max_length // next_ncol]
                                 )
                                 / (2 * current_root) )
                       current_root *= root
                 # Update
                 lowerCAmelCase    :		Any				=      new_inverse_c
                 next_ncol *= 2
           # Unpack
           lowerCAmelCase    :		Optional[int]				=      [round(x[0].real    , 8 ) + round(x[0].imag    , 8 ) * 1j for x in inverce_c]

           # Remove leading 0's
           while inverce_c[-1] == 0:
                 inverce_c.pop()
           return inverce_c






     def __str__(		self     :    int ):
           lowerCAmelCase    :		int				=      '''A = ''' + ''' + '''.join(
               F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A] ) )
           lowerCAmelCase    :		str				=      '''B = ''' + ''' + '''.join(
               F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B] ) )
           lowerCAmelCase    :		int				=      '''A*B = ''' + ''' + '''.join(
               F'''{coef}*x^{i}''' for coef, i in enumerate(self.product ) )

           return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()


