Moo Network

문제

Farmer John's $NN$ cows ($1\le N\le {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 10^5$) 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 $ii$th cow is located at a distinct location $(x_i,y_i)(x\_i,y\_i)$ where $0\le x_i\le {10}^{6}0\; \backslash leq\; x\_i\; \backslash leq\; 10^6$ and $0\le y_i\le 100\; \backslash leq\; y\_i\; \backslash leq\; 10$. The cost of building a communication link between cows $ii$ and $jj$ is the squared distance between them: $(x_i-x_j{)}^2+(y_i-y_j{)}^2(x\_i-x\_j)^2\; +\; (y\_i-y\_j)^2$.

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.

입력

The first line of input contains $NN$, and the next $NN$ lines each describe the $xx$ and $yy$ coordinates of a cow, all integers.

출력

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++).