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Tree Construction

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2488    Accepted Submission(s): 1371


Problem Description
Consider a two-dimensional space with a set of points (xi, yi) that satisfy xi < xj and yi > yj for all i < j. We want to have them all connected by a directed tree whose edges go toward either right (x positive) or upward (y positive). The figure below shows an example tree.


Write a program that finds a tree connecting all given points with the shortest total length of edges.
 

Input
The input begins with a line that contains an integer n (1 <= n <= 1000), the number of points. Then n lines follow. The i-th line contains two integers xi and yi (0 <= xi, yi <= 10000), which give the coordinates of the i-th point.
 

Output
Print the total length of edges in a line.
 

Sample Input
5 1 5 2 4 3 3 4 2 5 1 1 10000 0
 

Sample Output
12 0
 

Source
 

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