Bamboo Rectangles

Rahul, an algo-geek, went to Mizoram for a trip. There, while he was seeing the traditional dance with bamboos (Cheraw dance), he began thinking about algorithms (after all, he is an algo-geek!). He began wondering that given x and y co-ordinates of bottoms of a certain number of bamboo sticks of a particular length, with the sticks on x-axis placed vertically (parallel to the y-axis) and the stic