






import os






def   UpperCamelCase  (       ):




     '''simple docstring'''






     __snake_case			:List[str]          =						os.path.dirname(os.path.realpath(snake_case__  )  )
     __snake_case			:Union[str, Any]          =						os.path.join(snake_case__	,"""triangle.txt"""  )

     with open(snake_case__  ) as f:
          __snake_case			:int          =						f.readlines()

     __snake_case			:int          =						[]
     for line in triangle:
          __snake_case			:List[Any]          =						[]
          for number in line.strip().split(""" """  ):
               numbers_from_line.append(int(snake_case__  )  )
          a.append(snake_case__  )

     for i in range(1	,len(snake_case__  )  ):
          for j in range(len(a[i]  )  ):
               __snake_case			:Union[str, Any]          =						a[i - 1][j] if j != len(a[i - 1]  ) else 0
               __snake_case			:Dict          =						a[i - 1][j - 1] if j > 0 else 0
               a[i][j] += max(snake_case__	,snake_case__  )
     return max(a[-1]  )


if __name__ == "__main__":
     print(solution())










from __future__ import annotations

lowerCamelCase__							=     list[list[int]]

# assigning initial values to the grid
lowerCamelCase__							=     [
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCamelCase__							=     [
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]






def   UpperCamelCase  (       snake_case__     :   Matrix	,snake_case__     :   int	,snake_case__     :   int	,snake_case__     :   int  ):




     '''simple docstring'''






     for i in range(9  ):
          if grid[row][i] == n or grid[i][column] == n:
               return False

     for i in range(3  ):
          for j in range(3  ):
               if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
                    return False

     return True






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     for i in range(9  ):
          for j in range(9  ):
               if grid[i][j] == 0:
                    return i, j
     return None






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     if location := find_empty_location(snake_case__  ):
          __snake_case       , __snake_case			:Optional[int]          =						location
     else:
          # If the location is ``None``, then the grid is solved.
          return grid

     for digit in range(1	,10  ):
          if is_safe(snake_case__	,snake_case__	,snake_case__	,snake_case__  ):
               __snake_case			:Union[str, Any]          =						digit

               if sudoku(snake_case__  ) is not None:
                    return grid

               __snake_case			:Tuple          =						0

     return None






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     for row in grid:
          for cell in row:
               print(snake_case__	,end=""" """  )
          print()


if __name__ == "__main__":
     # make a copy of grid so that you can compare with the unmodified grid
     for example_grid in (initial_grid, no_solution):
          print("""\nExample grid:\n""" + """=""" * 20)
          print_solution(example_grid)
          print("""\nExample grid solution:""")
          lowerCamelCase__							=     sudoku(example_grid)
          if solution is not None:
               print_solution(solution)
          else:
               print("""Cannot find a solution.""")


