



"""simple docstring"""

lowercase__					:						Tuple												=			range(2, 20 + 1)
lowercase__					:						int												=			[10**k for k in range(ks[-1] + 1)]
lowercase__					:						List[Any]												=			{}




def __lowercase    (							_a	,    _a	,    _a	,    _a					):
    snake_case_				:  Tuple       =			sum(a_i[j] for j in range(__lowercase	,    len(__lowercase					)					)					)
    snake_case_				:  Any       =			sum(a_i[j] * base[j] for j in range(min(len(__lowercase					)	,    __lowercase					)					)					)

    snake_case_				:  str       =			0, 0
    snake_case_				:  List[Any]       =			n - i

    snake_case_				:  Tuple       =			memo.get(__lowercase					)

    if sub_memo is not None:
        snake_case_				:  Dict       =			sub_memo.get(__lowercase					)

        if jumps is not None and len(__lowercase					) > 0:
            # find and make the largest jump without going over
            snake_case_				:  Optional[Any]       =			-1
            for _k in range(len(__lowercase					) - 1	,    -1	,    -1					):
                if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
                    snake_case_				:  List[Any]       =			_k
                    break

            if max_jump >= 0:
                snake_case_				:  List[Any]       =			jumps[max_jump]
                # since the difference between jumps is cached, add c
                snake_case_				:  int       =			diff + c
                for j in range(min(__lowercase	,    len(__lowercase					)					)					):
                    snake_case_				:  Optional[Any]       =			divmod(__lowercase	,    10					)
                if new_c > 0:
                    add(__lowercase	,    __lowercase	,    __lowercase					)

        else:
            snake_case_				:  List[str]       =			[]
    else:
        snake_case_				:  Optional[int]       =			{c: []}
        snake_case_				:  List[str]       =			sub_memo

    if dn >= max_dn or c + diff >= base[k]:
        return diff, dn

    if k > ks[0]:
        while True:
            # keep doing smaller jumps
            snake_case_				:  int       =			next_term(__lowercase	,    k - 1	,    i + dn	,    __lowercase					)
            diff += _diff
            dn += terms_jumped

            if dn >= max_dn or c + diff >= base[k]:
                break
    else:
        # would be too small a jump, just compute sequential terms instead
        snake_case_				:  Optional[int]       =			compute(__lowercase	,    __lowercase	,    i + dn	,    __lowercase					)
        diff += _diff
        dn += terms_jumped

    snake_case_				:  Any       =			sub_memo[c]

    # keep jumps sorted by # of terms skipped
    snake_case_				:  Union[str, Any]       =			0
    while j < len(__lowercase					):
        if jumps[j][1] > dn:
            break
        j += 1

    # cache the jump for this value digitsum(b) and c
    sub_memo[c].insert(__lowercase	,    (diff, dn, k)					)
    return (diff, dn)




def __lowercase    (							_a	,    _a	,    _a	,    _a					):




    if i >= n:
        return 0, i
    if k > len(__lowercase					):
        a_i.extend([0 for _ in range(k - len(__lowercase					)					)]					)

    # note: a_i -> b * 10^k + c
    # ds_b -> digitsum(b)
    # ds_c -> digitsum(c)
    snake_case_				:  int       =			i
    snake_case_				:  Union[str, Any]       =			0, 0, 0
    for j in range(len(__lowercase					)					):
        if j >= k:
            ds_b += a_i[j]
        else:
            ds_c += a_i[j]

    while i < n:
        i += 1
        snake_case_				:  Tuple       =			ds_c + ds_b
        diff += addend
        snake_case_				:  List[Any]       =			0
        for j in range(__lowercase					):
            snake_case_				:  Optional[Any]       =			a_i[j] + addend
            snake_case_				:  Dict       =			divmod(__lowercase	,    10					)

            ds_c += a_i[j]

        if addend > 0:
            break

    if addend > 0:
        add(__lowercase	,    __lowercase	,    __lowercase					)
    return diff, i - start_i




def __lowercase    (							_a	,    _a	,    _a					):




    for j in range(__lowercase	,    len(__lowercase					)					):
        snake_case_				:  Optional[int]       =			digits[j] + addend
        if s >= 10:
            snake_case_				:  Union[str, Any]       =			divmod(__lowercase	,    10					)
            snake_case_				:  List[Any]       =			addend // 10 + quotient
        else:
            snake_case_				:  Union[str, Any]       =			s
            snake_case_				:  Optional[Any]       =			addend // 10

        if addend == 0:
            break

    while addend > 0:
        snake_case_				:  Dict       =			divmod(__lowercase	,    10					)
        digits.append(__lowercase					)




def __lowercase    (							_a = 10**15					):
    snake_case_				:  Optional[Any]       =			[1]
    snake_case_				:  Union[str, Any]       =			1
    snake_case_				:  Any       =			0
    while True:
        snake_case_				:  Dict       =			next_term(__lowercase	,    20	,    i + dn	,    __lowercase					)
        dn += terms_jumped
        if dn == n - i:
            break

    snake_case_				:  Any       =			0
    for j in range(len(__lowercase					)					):
        a_n += digits[j] * 10**j
    return a_n


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










"""simple docstring"""

import math
import sys

import cva
import numpy as np




def __lowercase    (							_a	,    _a					):
    # For applying gaussian function for each element in matrix.
    snake_case_				:  Dict       =			math.sqrt(_a					)
    snake_case_				:  Tuple       =			1 / (sigma * math.sqrt(2 * math.pi					))
    return cons * np.exp(-((img / sigma) ** 2) * 0.5					)




def __lowercase    (							_a	,    _a	,    _a	,    _a					):
    snake_case_				:  Optional[int]       =			kernel_size // 2
    return img[x - half : x + half + 1, y - half : y + half + 1]




def __lowercase    (							_a	,    _a					):
    # Creates a gaussian kernel of given dimension.
    snake_case_				:  Union[str, Any]       =			np.zeros((kernel_size, kernel_size)					)
    for i in range(0	,    _a					):
        for j in range(0	,    _a					):
            snake_case_				:  Union[str, Any]       =			math.sqrt(
                abs(i - kernel_size // 2					) ** 2 + abs(j - kernel_size // 2					) ** 2					)
    return vec_gaussian(_a	,    _a					)




def __lowercase    (							_a	,    _a	,    _a	,    _a	,    ):
    snake_case_				:  int       =			np.zeros(img.shape					)
    snake_case_				:  str       =			get_gauss_kernel(_a	,    _a					)
    snake_case_,			snake_case_				:  Any       =			img.shape
    for i in range(kernel_size // 2	,    size_x - kernel_size // 2					):
        for j in range(kernel_size // 2	,    size_y - kernel_size // 2					):
            snake_case_				:  List[Any]       =			get_slice(_a	,    _a	,    _a	,    _a					)
            snake_case_				:  Union[str, Any]       =			img_s - img_s[kernel_size // 2, kernel_size // 2]
            snake_case_				:  Optional[Any]       =			vec_gaussian(_a	,    _a					)
            snake_case_				:  Dict       =			np.multiply(_a	,    _a					)
            snake_case_				:  Dict       =			np.multiply(_a	,    _a					)
            snake_case_				:  List[Any]       =			np.sum(_a					) / np.sum(_a					)
            snake_case_				:  Dict       =			val
    return imga




def __lowercase    (							_a					):
    snake_case_				:  Optional[int]       =			args[1] if args[1:] else '''../image_data/lena.jpg'''
    snake_case_				:  int       =			float(args[2]					) if args[2:] else 1.0
    snake_case_				:  Dict       =			float(args[3]					) if args[3:] else 1.0
    if args[4:]:
        snake_case_				:  Optional[Any]       =			int(args[4]					)
        snake_case_				:  Union[str, Any]       =			kernel_size + abs(kernel_size % 2 - 1					)
    else:
        snake_case_				:  Union[str, Any]       =			5
    return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
     lowercase__					,lowercase__					,lowercase__					,lowercase__					:						Tuple												=			parse_args(sys.argv)
     lowercase__					:						str												=			cva.imread(filename, 0)
     cva.imshow('''input image''', img)

     lowercase__					:						Tuple												=			img / 2_55
     lowercase__					:						Optional[int]												=			out.astype('''float32''')
     lowercase__					:						Union[str, Any]												=			bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
     lowercase__					:						List[str]												=			out * 2_55
     lowercase__					:						List[str]												=			np.uinta(out)
     cva.imshow('''output image''', out)
     cva.waitKey(0)
     cva.destroyAllWindows()





