Editorial showed a algorithm to build $$$min(\text{black cells}, \text{white cells})$$$ dominos. The proof for the algorithm uses the fact that the histogram is sorted, so two equal rows are always adjacent.

Without affecting the answer, we add '0' at the end of the histogram.

We define two operations:

1. If the difference between neighbour two bars $$$ \geq 2 $$$, then delete vertical dominos to reduce the difference.
   Example: 8 7 3 1 -> 8 7 1 1 -> 8 1 1 1 -> 2 1 1 1
2. Choose the rightmost two neighbour bars that have the same height. Delete the horizontal domino on the top.
   Example: 3 2 2 1 -> 3 1 1 1 -> 3 1 0 0

Repeatedly do the operation (1) and (2) until you can't. Note if no neighbour difference $$$ \geq 2 $$$ or $$$ = 0 $$$, then all neighbour difference $$$ = 1 $$$, which is "basic diagram" stated at the editorial. We then can just choose all dominos vertically on the "basic diagram".