Doors

Doors (Seethrough, Open Doors) is a logic puzzle. Determine whether the doors between each of the two rooms are open or closed.

Rules: Each cell in the grid represents a room in a building; there is a door between two orthogonally adjacent rooms. The number in a room indicates how many other rooms you can see in total when looking north, south, east, and west.
All rooms must form a single orthogonal area. Determine which door is closed and which is open.