Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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

Solution in Ruby (judge verdict: Wrong Answer)

ary = {}
gets.to_i.times {
    a = gets.split(" ").map {|s| s.to_i }
    (a[0]...a[2]).each {|x|
        (a[1]...a[3]).each{|y|
            ary[x] = [] if ary[x].nil?
            ary[x] << y
        }
    }
}

puts ary.map {|a| a.nil? ? 0 : a.uniq.count }#.reduce {|sum, n| sum + n }