POJ ３２６９ Building A New Barn

Building A New Barn

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 1886		Accepted: 609

Description

After scrimping and saving for years, Farmer John has decided to build a new barn. He wants the barn to be highly accessible, and he knows the coordinates of the grazing spots of all N (2 ≤ N ≤ 10,000 cows. Each grazing spot is at a point with integer coordinates (X_i, Y_i) (-10,000 ≤ X_i ≤ 10,000; -10,000 ≤ Y_i ≤ 10,000). The hungry cows never graze in spots that are horizontally or vertically adjacent.

The barn must be placed at integer coordinates and cannot be on any cow's grazing spot. The inconvenience of the barn for any cow is given the Manhattan distance formula | X - X_i | + | Y - Y_i|, where (X, Y) and (X_i, Y_i) are the coordinates of the barn and the cow's grazing spot, respectively. Where should the barn be constructed in order to minimize the sum of its inconvenience for all the cows?

Input

Line 1: A single integer:  N 
Lines 2.. N+1: Line  i+1 contains two space-separated integers which are the grazing location ( X_i,  Y_i) of cow  i

Output

Line 1: Two space-separated integers: the minimum inconvenience for the barn and the number of spots on which Farmer John can build the barn to achieve this minimum.

Sample Input

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

Sample Output

10 4

Hint

The minimum inconvenience is 10, and there are 4 spots that Farmer John can build the farm to achieve this: (0, -1), (0, 0), (1, 0), and (1, 1).

Source

USACO 2007 February Gold