title: Maximum rectangle overlapping point
body: <p>Given the coordinates of N rectangles (N&lt;=100.000) in the grid L*C (L and C can range from 0 to 1.000.000.000) I want to know what is the maximum number of rectangle overlapping at any point in the grid.</p>
  
  <p>So I figured I would use a sweeping algorithm, for each event (opening or ending of a rectangle) sorted by x value, I  add or remove an interval to my structure.</p>
  
  <p>I have to use a tree to maintain the maximum overlapping of the intervals, and be able to add and remove an interval. </p>
  
  <p>I know how to do that when the values of the intervals (start and end) are ranging from 0 to 100.000, but it is impossible here since the dimensions of the plane are from 0 to 1.000.000.000. How can I implement such a tree?</p>