SP14848 BOXLINGS - Boxlings

Doctor Y, always eager to further his research in the field of boxology, is observing a family of boxen in their natural habitat – a barrel of wine. He has noticed that in addition to the $ N $ ( $ 1 \leq N \leq 200,000 $ ) rectangular, two-dimensional boxen, there are $ M $ ( $ 1 \leq M \leq 200,000 $ ) almost imperceptible points floating on the surface of the wine. He reasons that these must be baby boxen – also known as boxlings. Curious as to the customs of box families, Doctor Y wishes to count how many boxlings are floating on top of boxen. From his top-down view of the barrel, he has divided the surface of the wine into a two-dimensional Cartesian plane, and noted the positions of all the boxen and boxlings. Each box occupies a rectangular region parallel to the axes of the plane, with two of its opposite corners at coordinates ( $ x_1 $ , $ y_1 $ ) and ( $ x_2 $ , $ y_2 $ ). Doctor Y has observed that boxen sometimes overlap with one another. On the other hand, each boxling is so small that it occupies only a single point on the plane, with x-coordinate $ a $ and y-coordinate $ b $ . All coordinates have absolute values no larger than $ 10^9 $ . Having recorded the locations of all of the life forms on the surface of the wine, Doctor Y is interested in counting exactly how many boxlings are floating on top of at least one box. Note that if a boxling is on the very edge or corner of a box, it counts as being on top. Also note that two boxlings can occupy the exact same locations, in which case they should still be counted separately. It's also possible for a box to have zero area, in which case it's treated as a line (or point) and can still have boxlings on top of it. With so many boxen and boxlings living in this wine barrel, Doctor Y doesn’t feel like sitting there and counting them all by hand, crazy though he is. As such, he wants you to write a program to, given the locations of all the boxen and boxlings, count the number of boxlings that are floating on top of at least one box. Don’t worry - your hard work will surely lead to exciting discoveries in the field of boxology.

Line $ 1 $ : 2 integers, $ N $ and $ M $ Next $ N $ lines: 4 integers, $ x_1 $ , $ y_1 $ , $ x_2 $ , and $ y_2 $ , the coordinates of each box Next $ M $ lines: 2 integers, $ a $ and $ b $ , the coordinates of each boxling

A single integer – the number of boxlings that are on top of at least one box.