




from __future__ import annotations

def      A      (      _SCREAMING_SNAKE_CASE    )	-> int:

       # preprocessing the first row
       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(_SCREAMING_SNAKE_CASE    )    ):
              matrix[i][0] += matrix[i - 1][0]

       # updating the path cost for current position
       for i in range(1 ,len(_SCREAMING_SNAKE_CASE    )    ):
              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()












from math import sqrt

def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> int:
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int

       while num_cuboids <= limit:
              max_cuboid_size += 1
              for sum_shortest_sides in range(2 ,2 * max_cuboid_size + 1    ):
                     if sqrt(sum_shortest_sides**2 + max_cuboid_size**2    ).is_integer():
                            num_cuboids += (
                                min(_SCREAMING_SNAKE_CASE ,sum_shortest_sides // 2    )
                                - max(1 ,sum_shortest_sides - max_cuboid_size    )
                                + 1
                            )

       return max_cuboid_size


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






