
from __future__ import annotations






def 						__magic_name__			(   __a      :	Tuple	,		__a      :	List[str]	,		__a      :	Optional[int]	,		__a      :	str						):  # noqa: E741



     '''simple docstring'''




     while r - l > 1:
          UpperCamelCase__				=    (l + r) // 2
          if v[m] >= key:
               UpperCamelCase__				=    m
          else:
               UpperCamelCase__				=    m  # noqa: E741
     return r






def 						__magic_name__			(   __a      :	list[int]						):



     '''simple docstring'''




     if len(__a						) == 0:
          return 0

     UpperCamelCase__				=    [0] * len(__a						)
     UpperCamelCase__				=    1

     UpperCamelCase__				=    v[0]

     for i in range(1	,		len(__a						)						):
          if v[i] < tail[0]:
               UpperCamelCase__				=    v[i]
          elif v[i] > tail[length - 1]:
               UpperCamelCase__				=    v[i]
               length += 1
          else:
               UpperCamelCase__				=    v[i]

     return length


if __name__ == "__main__":
    import doctest

    doctest.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()





