Number In Order

Example puzzle on the left, solution on the right

Number In Order is a puzzle original to this blog to the best of my knowledge.

1. Put a positive integer into each white cell.
2. Define a “run of cells” be some white cells that are in the same row or column, and are all connected (not separated by black cells).
3. The maximum integer can be put on the puzzle is the size of the largest run of cells.
4. Each run of cell must contain at most one instance of every integer. Moreover, all the integers in a run of cells must be consecutive.