
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()







def 						__magic_name__			(   __a      :	int	,		__a      :	int						):



     '''simple docstring'''




     while a != 0:
          UpperCamelCase__		,	UpperCamelCase__				=    b % a, a
     return b






def 						__magic_name__			(   __a      :	int	,		__a      :	int						):



     '''simple docstring'''




     if gcd(__a	,		__a						) != 1:
          UpperCamelCase__				=    f"mod inverse of {a!r} and {m!r} does not exist"
          raise ValueError(__a						)
     UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    1, 0, a
     UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    0, 1, m
     while va != 0:
          UpperCamelCase__				=    ua // va
          UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__				=    (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
     return ua % m





