Conspicuous buildings

In a city, all the buildings are located in the same district.

This district is a rectangle of size W by H, its sides are labelled South, East, North and West.

• Each building occupies a 1-unit square, there are W*H buildings.
• There height are all integers from 1 to W*H.
• When we look at the buildings facing South face or East face, we can see each building, partly or totally. No building is hidden behind a higher one.

For a 2*3 rectangle, there are five possible arrangements for the buildings.



How many possible arrangements are there for a 15*20 rectangle?


Answer format: the count in compressed format as in problem 198.
[My timing: < 100 ms]