
import math






def 						__magic_name__			(   __a      :	float	,		__a      :	float						):



     '''simple docstring'''




     return math.pow(__a	,		2						) - a






def 						__magic_name__			(   __a      :	float						):



     '''simple docstring'''




     return 2 * x






def 						__magic_name__			(   __a      :	float						):



     '''simple docstring'''




     UpperCamelCase__				=    2.0

     while start <= a:
          UpperCamelCase__				=    math.pow(__a	,		2						)

     return start






def 						__magic_name__			(   __a      :	float	,		__a      :	int = 9_999	,		__a      :	float = 0.00_000_000_000_001						):



     '''simple docstring'''




     if a < 0:
          raise ValueError("""math domain error"""						)

     UpperCamelCase__				=    get_initial_point(__a						)

     for _ in range(__a						):
          UpperCamelCase__				=    value
          UpperCamelCase__				=    value - fx(__a	,		__a						) / fx_derivative(__a						)
          if abs(prev_value - value						) < tolerance:
               return value

     return value


if __name__ == "__main__":
    from doctest import testmod

    testmod()







from __future__ import annotations






def 						__magic_name__			(   __a      :	list[list[int]]						):



     '''simple docstring'''




     for i in range(1	,		len(matrix[0]						)						):
          matrix[0][i] += matrix[0][i - 1]

     # preprocessing the first column
     for i in range(1	,		len(__a						)						):
          matrix[i][0] += matrix[i - 1][0]

     # updating the path cost for current position
     for i in range(1	,		len(__a						)						):
          for j in range(1	,		len(matrix[0]						)						):
               matrix[i][j] += min(matrix[i - 1][j]	,		matrix[i][j - 1]						)

     return matrix[-1][-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()





