def is_proper_position(dimension, position):
    """
        Check whether the given position is a proper position for any board
        with the given dimension.
        - The given position must be a tuple of length 2 whose elements are both
          natural numbers.
        - The first element identifies the column. It may not exceed the given
          dimension.
        - The second element identifies the row. It may not exceed the given
          dimension incremented with 1 (taking into account the overflow position)
        ASSUMPTIONS
        - None
    """
    if not isinstance(position, tuple) or len(position) != 2:
        return False

    if position[0] <= 0 or position[1] <= 0:  # Negative integer
        return False

    if position[0] > dimension or position[1] > dimension + 1:  # Greater than dimension
        return False
    return True