Skyscrapers Either Or (Mini Puzzles Series #33)

This puzzle type appeared in World Puzzle Championship 2009 which was the 18th World Puzzle Championship, Antalya (Turkey). This puzzle was one of the few puzzles of this type that I created for the practice of the Indian Puzzle Team participating in the World Puzzle Championship 2009. Now I am re-publishing this puzzle as the 33rd puzzle in Mini Puzzles Series. Can you solve this Skyscrapers Either Or puzzle?

Rules of Skyscrapers Either Or puzzle

Fill in each cell of the grid with digits 1-4, so that each digit appears exactly once in each row and in each column. Each digit inside the grid represents a building with the height of the digit itself. Numbers outside the grid indicate EITHER a)the number of buildings that can be seen by an observer looking into the grid in the corresponding direction, taking into account that higher buildings block the view of lower buildings from the observer, OR b)the height of the first visible building in that direction.