Washer

You have $n$ clothes and a washer. The washer is large enough to wash all the clothes at once. However, you have to worry about color transfer: if you put clothes of different colors in the washer, the dye from one may stain another. Precisely, let $r_i$, $g_i$, $b_i$ denote the amount of red, green, blue color of the $i$-th clothes. When $n$ clothes are washed together, the color transfer $c$ is defined by

$c = \sum_{i=1}^{n}{(r_i - r)^2 + (g_i - g)^2 + (b_i - b)^2}$

where $r$, $g$, and $b$ are the averages of $r_i$, $g_i$, $b_i$, respectively. The $i$-th clothes with $r_i$, $g_i$, and $b_i$ is defined as a point $(r_i, g_i, b_i)$ in 3-dimensional RGB space. You can assume that no three points (clothes) are on a same line and no four points (clothes) are on a same plane in RGB space.

The washer consumes a lot of electricity, and you have to partition $n$ clothes into at most $k$ groups, and run the washer for each group. The total color transfer is the sum of color transfers from each run. Given the color information of $n$ clothes and $k$, write a program to calculate the minimum total color transfer.

Your program is to read from standard input. The first line contains two integers $n$ (1 ≤ $n$ ≤ 100) and $k$ (1 ≤ $k$ ≤ 2). In the following $n$ lines, the $i$-th line contains three integers $r_i$, $g_i$, $b_i$ (0 ≤ $r_i$, $g_i$, $b_i$ ≤ 1,000).

Your program is to write to standard output. Print exactly one line containing the minimum total color transfer, rounded to the sixth decimal point.