Description
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.
Input
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
Output
Write a single integer specifying amount of total area FJ can save by using two enclosures instead o
f one.
Sample Input
64 2
8 10
1 1
9 12
14 7
2 3
