Minimize Total Grid Distance to Every Building

Given a rectangular grid containing buildings, empty land, and obstacles, choose an empty cell that minimizes the sum of its shortest-path distances to every building. Return that minimum sum, or `-1` if no empty cell can reach every building. ### Input - `grid`: a two-dimensional integer array. A `0` is empty land, a `1` is a building, and a `2` is an obstacle. ### Output Return the minimum total distance as an integer. Return only the distance, so tied locations do not require a tie-break. ### Constraints and Edge Cases - For this practice version, the grid has between `1` and `50` rows and between `1` and `50` columns. - At least one building is present. - One move enters an orthogonally adjacent cell and has cost one. Diagonal movement is not allowed. - Intermediate cells on a path must be empty land. A building may be the destination, but a path cannot pass through it to reach another building. - Obstacles cannot be entered. - If no empty land exists, or no empty cell reaches every building, return `-1`. ### Example 1 ```text grid = [[1,0,2], [0,0,0], [2,0,1]] output = 4 ``` The center cell has distance two to each building, for a total of four. No candidate has a smaller sum. ### Example 2 ```text grid = [[1,0,1,0,1]] output = -1 ``` The middle building blocks travel between the two empty cells. Neither candidate can reach all three buildings without passing through a building.