Coordinate Compression - Union of Rectangles

Time Limit : 6 sec, Memory Limit : 262144 KB
Japanese version is here

Union of Rectangles

Given a set of $N$ axis-aligned rectangles in the plane, find the area of regions which are covered by at least one rectangle.

Input

The input is given in the following format.

$N$
$x1_1$ $y1_1$ $x2_1$ $y2_1$
$x1_2$ $y1_2$ $x2_2$ $y2_2$
:
$x1_N$ $y1_N$ $x2_N$ $y2_N$

($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left corner and the bottom-right corner of the $i$-th rectangle respectively.

Constraints

  • $ 1 \leq N \leq 2000 $
  • $ |10^9 \leq x1_i < x2_i\leq 10^9 $
  • $ |10^9 \leq y1_i < y2_i\leq 10^9 $

Output

Print the area of the regions.

Sample Input 1

2
0 0 3 4
1 2 4 3

Sample Output 1

13

Sample Input 2

3
1 1 2 5
2 1 5 2
1 2 2 5

Sample Output 2

7

Sample Input 3

4
0 0 3 1
0 0 1 3
0 2 3 3
2 0 3 3

Sample Output 3

8