Add One Source to Minimize Grid Inconvenience

Implement min_max_inconvenience(grid).

grid is a non-empty rectangular matrix containing 0 and 1. A cell containing 1 is an existing colored source. You may choose any one cell, including an already colored cell, and add a colored source there.

Movement is allowed in all eight directions: horizontal, vertical, and diagonal. Every move costs one. A cell's inconvenience is its shortest-path distance to the nearest colored source after your addition. Return the smallest possible value of the maximum inconvenience over all cells.

Examples

• For [[0]], return 0.
• For [[1, 0, 0]], return 1 by adding a source at the last cell.
• For [[1, 0], [0, 0]], return 1; after adding one source, at least one uncolored cell remains one move from its nearest source.

Constraints

• 1 <= len(grid), len(grid[0]) <= 200
• Every row has the same length.
• Every element is either 0 or 1.
• The grid may initially contain no colored source.