P2956 [USACO09OCT] The Robot Plow G

Farmer John has purchased a new robotic plow in order to relieve him from the drudgery of plowing field after field after field. It achieves this goal but at a slight disadvantage: the robotic plow can only plow in a perfect rectangle with sides of integer length. Because FJ's field has trees and other obstacles, FJ sets up the plow to plow many different rectangles, which might end up overlapping. He's curious as to just how many squares in his field are actually plowed after he programs the plow with various plow instructions, each of which describes a rectangle by giving its lower left and upper right x,y coordinates. As usual, the field is partitioned into squares whose sides are parallel to the x and y axes. The field is X squares wide and Y squares high (1

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As in the task's example.