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50989 - Rectangles and Points

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

Rectangles and Points

Question: You are given coordinates of n rectangles. Then you are also given m points. List top k rectangles which overlap with the most number of points. If two rectangles have the same number of overlapping points, list them according to the order of appearance. Note: 1) The point is count overlapping, alsowhen it is on any edge of the rectangle. 2) The corners are random; they are not guaranteed to be in any order.

Input specification: In the first line, you will be given three integers: the number of rectangles (n), the number of points (m) and the number of top (k) rectangles to list. The following n lines will contain 4 integers (x1, y1, x2, y2). Then, the following m lines will contain 2 integers (x, y) where 1 ≤ (m, n) ≤ 8,000.

Output specification: Show k integers (order of rectangles).

Sample Input
4 6 2
4 7 7 12
5 4 8 13
3 2 7 8
4 4 12 6
5 7
6 7
1 6
10 7
2 8
3 2
Sample Output
3 1

Explanation: There are four rectangles and 6 points given. The first, the second and the third rectangles overlap with two points (5, 7) and (6, 7). The third rectangle also overlaps with (3,2). The fourth rectangle does not overlap with any points. So, the top two rectangles are 3 (overlapping with 3 points) and 1 (overlapping with 2 points).



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