8578: BZOJ4578：[Usaco2016 OPen]Splitting the Field

Farmer John's N cows (3≤N≤50,000) are all located at distinct positions in his two-dimensional fie ld. FJ wants to enclose all of the cows with a rectangular fence whose sides are parallel to the x a nd y axes, and he wants this fence to be as small as possible so that it contains everycow (cows on  the boundary are allowed).FJ is unfortunately on a tight budget due to low milk production last quar ter. He would therefore like to enclose a smaller area to reduce maintenance costs, and the only way  he can see to do this is by building two enclosures instead of one. Please help him compute how muc h less area he needs to enclose, in total, by using two enclosures instead of one. Like the original  enclosure, the two enclosures must collectively contain all the cows (with cows on boundaries allow ed), and they must have sides parallel to the x and y axes. The two enclosures are notallowed to ove rlap -- not even on their boundaries. Note that enclosures of zero area are legal, for example if an  enclosure has zero width and/or zero height.

输入格式

The first line of input contains N. The nextNN lines each contain two integers specifying the location of a cow. Cow locations are positive integers in the range 1…1,000,000,000

输出格式

Write a single integer specifying amount of total area FJ can save by using two enclosures instead o f one.

样例输入

6
4 2
8 10
1 1
9 12
14 7
2 3

样例输出

107

提示

没有写明提示

题目来源

Gold