

def a_		(       UpperCamelCase_   :							int = 1_0_0  )							->   int:







 """simple docstring"""

 lowerCamelCase      						=    [[0 for _ in range(UpperCamelCase_  )] for _ in range(m + 1  )]
 for i in range(m + 1  ):
  lowerCamelCase      						=    1

 for n in range(m + 1  ):
  for k in range(1   ,					UpperCamelCase_  ):
   memo[n][k] += memo[n][k - 1]
   if n > k:
    memo[n][k] += memo[n - k - 1][k]

 return memo[m][m - 1] - 1


if __name__ == "__main__":
     print(solution(int(input('Enter a number: ').strip())))







import numpy as np
from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey

from digital_image_processing.filters.convolve import img_convolve







def a_		(       UpperCamelCase_   :							Dict  )							->   str:







 """simple docstring"""

 lowerCamelCase      						=    np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]  )
 lowerCamelCase      						=    np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]  )

 lowerCamelCase      						=    np.abs(img_convolve(UpperCamelCase_   ,					UpperCamelCase_  )  )
 lowerCamelCase      						=    np.abs(img_convolve(UpperCamelCase_   ,					UpperCamelCase_  )  )
 # modify the pix within [0, 255]
 lowerCamelCase      						=    dst_x * 2_5_5 / np.max(UpperCamelCase_  )
 lowerCamelCase      						=    dst_y * 2_5_5 / np.max(UpperCamelCase_  )

 lowerCamelCase      						=    np.sqrt((np.square(UpperCamelCase_  )) + (np.square(UpperCamelCase_  ))  )
 lowerCamelCase      						=    dst_xy * 2_5_5 / np.max(UpperCamelCase_  )
 lowerCamelCase      						=    dst_xy.astype(np.uinta  )

 lowerCamelCase      						=    np.arctana(UpperCamelCase_   ,					UpperCamelCase_  )
 return dst, theta


if __name__ == "__main__":
     # read original image
     _lowerCAmelCase :	Any     				=    imread('../image_data/lena.jpg')
     # turn image in gray scale value
     _lowerCAmelCase :	Optional[int]     				=    cvtColor(img, COLOR_BGR2GRAY)

     _lowerCAmelCase				,   _lowerCAmelCase :	Union[str, Any]     				=    sobel_filter(gray)

     # show result images
     imshow('sobel filter', sobel_grad)
     imshow('sobel theta', sobel_theta)
     waitKey(0)




