
from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase = 1 / sqrt(2	)	) ->						IIRFilter:
    __lowercase		:			List[Any]	    =       tau * frequency / samplerate
    __lowercase		:			Dict	    =       sin(__lowerCAmelCase	)
    __lowercase		:			Optional[int]	    =       cos(__lowerCAmelCase	)
    __lowercase		:			List[Any]	    =       _sin / (2 * q_factor)

    __lowercase		:			Tuple	    =       (1 - _cos) / 2
    __lowercase		:			Any	    =       1 - _cos

    __lowercase		:			int	    =       1 + alpha
    __lowercase		:			int	    =       -2 * _cos
    __lowercase		:			List[str]	    =       1 - alpha

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


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase = 1 / sqrt(2	)	) ->						IIRFilter:
    __lowercase		:			Tuple	    =       tau * frequency / samplerate
    __lowercase		:			List[str]	    =       sin(__lowerCAmelCase	)
    __lowercase		:			Dict	    =       cos(__lowerCAmelCase	)
    __lowercase		:			int	    =       _sin / (2 * q_factor)

    __lowercase		:			Union[str, Any]	    =       (1 + _cos) / 2
    __lowercase		:			Any	    =       -1 - _cos

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

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


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase = 1 / sqrt(2	)	) ->						IIRFilter:
    __lowercase		:			Any	    =       tau * frequency / samplerate
    __lowercase		:			Dict	    =       sin(__lowerCAmelCase	)
    __lowercase		:			Dict	    =       cos(__lowerCAmelCase	)
    __lowercase		:			Dict	    =       _sin / (2 * q_factor)

    __lowercase		:			Optional[Any]	    =       _sin / 2
    __lowercase		:			int	    =       0
    __lowercase		:			Optional[int]	    =       -ba

    __lowercase		:			Tuple	    =       1 + alpha
    __lowercase		:			int	    =       -2 * _cos
    __lowercase		:			str	    =       1 - alpha

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


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase = 1 / sqrt(2	)	) ->						IIRFilter:
    __lowercase		:			List[Any]	    =       tau * frequency / samplerate
    __lowercase		:			int	    =       sin(__lowerCAmelCase	)
    __lowercase		:			Any	    =       cos(__lowerCAmelCase	)
    __lowercase		:			Optional[Any]	    =       _sin / (2 * q_factor)

    __lowercase		:			Dict	    =       1 - alpha
    __lowercase		:			Dict	    =       -2 * _cos
    __lowercase		:			Tuple	    =       1 + alpha

    __lowercase		:			int	    =       IIRFilter(2	)
    filt.set_coefficients([ba, ba, ba]	,					[ba, ba, ba]	)
    return filt


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase = 1 / sqrt(2	)	,					) ->						IIRFilter:
    __lowercase		:			int	    =       tau * frequency / samplerate
    __lowercase		:			str	    =       sin(__lowerCAmelCase	)
    __lowercase		:			Tuple	    =       cos(__lowerCAmelCase	)
    __lowercase		:			Any	    =       _sin / (2 * q_factor)
    __lowercase		:			Any	    =       10 ** (gain_db / 40)

    __lowercase		:			Optional[Any]	    =       1 + alpha * big_a
    __lowercase		:			Optional[int]	    =       -2 * _cos
    __lowercase		:			Optional[Any]	    =       1 - alpha * big_a
    __lowercase		:			List[Any]	    =       1 + alpha / big_a
    __lowercase		:			int	    =       -2 * _cos
    __lowercase		:			int	    =       1 - alpha / big_a

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


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

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

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





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

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

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




from __future__ import annotations


def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						int:
    if not nums:
        return 0
    __lowercase		:			List[Any]	    =       nums[0]
    __lowercase		:			Union[str, Any]	    =       0
    for num in nums[1:]:
        __lowercase    ,      __lowercase		:			Dict	    =       (
            max_excluding + num,
            max(__lowerCAmelCase	,					__lowerCAmelCase	),
        )
    return max(__lowerCAmelCase	,					__lowerCAmelCase	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()


