Moo Network
Farmer John's N cows (1≤N≤105) are spread far apart on his farm and would like to build a communication network so they can more easily exchange electronic text messages (all of which of course contain variations of "moo").
The ith cow is located at a distinct location (xi,yi) where 0≤xi≤106 and 0≤yi≤10. The cost of building a communication link between cows i and j is the squared distance between them: (xi−xj)2+(yi−yj)2.
Please calculate the minimum cost required to build a communication network across which all the cows can communicate. Two cows can communicate if they are directly connected by a link, or if there is a sequence of links along which their message can travel.
**Note: the time limit for this problem is 4s, twice the default.**
SCORING:
- Test cases 2-3 satisfy N≤1000.
- Test cases 4-15 satisfy no additional constraints.
Problem credits: Brian Dean
Source: USA Computing Olympiad.
Input Format
The first line of input contains N, and the next N lines each describe the x and y coordinates of a cow, all integers.
Output Format
Please output the minimum cost of a network that will allow all cows to communicate. Note that this cost might be too large to fit into a 32-bit integer and may require use of 64-bit integers (e.g., "long long" integers in C++).