Farmer John's NN cows (1≤N≤1051≤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 iith cow is located at a distinct location (xi,yi**)(xi,yi) where 0≤xi≤1060≤xi≤106 and 0≤yi≤100≤yi≤10. The cost of building a communication link between cows ii and jj is the squared distance between them: (xi−xj)2+(yi−yj**)2(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.

INPUT FORMAT (input arrives from the terminal / stdin):

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

OUTPUT FORMAT (print output to the terminal / stdout):

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++).

SAMPLE INPUT:

10
83 10
77 2
93 4
86 6
49 1
62 7
90 3
63 4
40 10
72 0

SAMPLE OUTPUT:

660

SCORING:

• Test cases 2-3 satisfy N≤1000N≤1000.
• Test cases 4-15 satisfy no additional constraints.