'''simple docstring'''




import sys

_lowercase		:				Dict	       =		(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)




def 							lowerCamelCase			(   UpperCAmelCase__ :      str				)    ->   int:
							lowercase_      :    str       		= 1
							for digit in s:
														product *= int(UpperCAmelCase__				)
							return product




def 							lowerCamelCase			(   UpperCAmelCase__ :      str = N				)    ->   int:
							lowercase_      :    Optional[int]       		= -sys.maxsize - 1
							lowercase_      :    str       		= n[:13]
							lowercase_      :    Optional[int]       		= 13
							while cur_index < len(UpperCAmelCase__				) - 13:
														if int(n[cur_index]				) >= int(substr[0]				):
																					lowercase_      :    Optional[int]       		= substr[1:] + n[cur_index]
																					cur_index += 1
														else:
																					lowercase_      :    Optional[int]       		= max(UpperCAmelCase__   ,   str_eval(UpperCAmelCase__				)				)
																					lowercase_      :    Dict       		= n[cur_index : cur_index + 13]
																					cur_index += 13
							return largest_product


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






'''simple docstring'''




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    int       		= cos(UpperCAmelCase__				)
							lowercase_      :    Any       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 - _cos) / 2
							lowercase_      :    Optional[int]       		= 1 - _cos

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    List[Any]       		= -2 * _cos
							lowercase_      :    Union[str, Any]       		= 1 - alpha

							lowercase_      :    List[Any]       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Optional[int]       		= sin(UpperCAmelCase__				)
							lowercase_      :    Dict       		= cos(UpperCAmelCase__				)
							lowercase_      :    Optional[int]       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 + _cos) / 2
							lowercase_      :    str       		= -1 - _cos

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Optional[Any]       		= -2 * _cos
							lowercase_      :    List[Any]       		= 1 - alpha

							lowercase_      :    Union[str, Any]       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    int       		= tau * frequency / samplerate
							lowercase_      :    int       		= sin(UpperCAmelCase__				)
							lowercase_      :    Union[str, Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    str       		= _sin / (2 * q_factor)

							lowercase_      :    str       		= _sin / 2
							lowercase_      :    Any       		= 0
							lowercase_      :    Optional[Any]       		= -ba

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Union[str, Any]       		= -2 * _cos
							lowercase_      :    Union[str, Any]       		= 1 - alpha

							lowercase_      :    Tuple       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    List[str]       		= tau * frequency / samplerate
							lowercase_      :    Any       		= sin(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    Optional[Any]       		= _sin / (2 * q_factor)

							lowercase_      :    Any       		= 1 - alpha
							lowercase_      :    Optional[Any]       		= -2 * _cos
							lowercase_      :    Optional[int]       		= 1 + alpha

							lowercase_      :    Dict       		= IIRFilter(2				)
							filt.set_coefficients([ba, ba, ba]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    Dict       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= _sin / (2 * q_factor)
							lowercase_      :    Any       		= 10 ** (gain_db / 40)

							lowercase_      :    List[str]       		= 1 + alpha * big_a
							lowercase_      :    List[Any]       		= -2 * _cos
							lowercase_      :    Dict       		= 1 - alpha * big_a
							lowercase_      :    str       		= 1 + alpha / big_a
							lowercase_      :    List[str]       		= -2 * _cos
							lowercase_      :    Tuple       		= 1 - alpha / big_a

							lowercase_      :    Any       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    Dict       		= tau * frequency / samplerate
							lowercase_      :    Union[str, Any]       		= sin(UpperCAmelCase__				)
							lowercase_      :    Any       		= cos(UpperCAmelCase__				)
							lowercase_      :    Any       		= _sin / (2 * q_factor)
							lowercase_      :    Any       		= 10 ** (gain_db / 40)
							lowercase_      :    Any       		= (big_a + 1) - (big_a - 1) * _cos
							lowercase_      :    int       		= (big_a + 1) + (big_a - 1) * _cos
							lowercase_      :    Tuple       		= (big_a - 1) - (big_a + 1) * _cos
							lowercase_      :    Optional[Any]       		= (big_a - 1) + (big_a + 1) * _cos
							lowercase_      :    int       		= 2 * sqrt(UpperCAmelCase__				) * alpha

							lowercase_      :    Tuple       		= big_a * (pmc + aaa)
							lowercase_      :    List[str]       		= 2 * big_a * mpc
							lowercase_      :    Union[str, Any]       		= big_a * (pmc - aaa)
							lowercase_      :    Optional[int]       		= ppmc + aaa
							lowercase_      :    Optional[int]       		= -2 * pmpc
							lowercase_      :    Any       		= ppmc - aaa

							lowercase_      :    Optional[int]       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    int       		= sin(UpperCAmelCase__				)
							lowercase_      :    int       		= cos(UpperCAmelCase__				)
							lowercase_      :    Dict       		= _sin / (2 * q_factor)
							lowercase_      :    Union[str, Any]       		= 10 ** (gain_db / 40)
							lowercase_      :    Union[str, Any]       		= (big_a + 1) - (big_a - 1) * _cos
							lowercase_      :    Optional[int]       		= (big_a + 1) + (big_a - 1) * _cos
							lowercase_      :    Any       		= (big_a - 1) - (big_a + 1) * _cos
							lowercase_      :    str       		= (big_a - 1) + (big_a + 1) * _cos
							lowercase_      :    Optional[int]       		= 2 * sqrt(UpperCAmelCase__				) * alpha

							lowercase_      :    Tuple       		= big_a * (ppmc + aaa)
							lowercase_      :    List[Any]       		= -2 * big_a * pmpc
							lowercase_      :    Optional[Any]       		= big_a * (ppmc - aaa)
							lowercase_      :    Optional[Any]       		= pmc + aaa
							lowercase_      :    int       		= 2 * mpc
							lowercase_      :    Tuple       		= pmc - aaa

							lowercase_      :    Union[str, Any]       		= IIRFilter(2				)
							filt.set_coefficients([aa, aa, aa]   ,   [ba, ba, ba]				)
							return filt





