Chaos Construction: Numbered Rooms / Skyscraper / Sandwich Length

Rules:

Place the numbers from 1 to 9 exactly once in every row, column, and region. One number is already given. Each region is orthogonally connected and must be located by the solver.

A clue outside the grid can mean one of three things, as written below.

Numbered Rooms:

A clue outside the grid indicates the number which has to be placed in the Nth cell in the corresponding direction, where N is the number placed closest to the clue. Both the indexing number and the indexed number are in the same region.

Skyscraper:

Treat each number N as a building of height N. A clue outside the grid indicates the number of buildings seen from from that direction, where taller buildings hide shorter buildings. Each seen building is in a different region.

Sandwich Length:

A clue outside the grid indicates the number of cells between the 1 and the 9 in that row or column. The numbers between the 1 and the 9 in that row or column are all in the same region, and that region does not include either the 1 or the 9 in the respective row or column.