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1 초 512 MB 127 28 22 19.469%

문제

You have n clothes and a washer. The washer is large enough to wash all clothes at once. However, we should worry about the color transfer: if we put clothes of different colors in the washer, the dye from one may stain another. Precisely, let ri, gi, bi 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 ri, gi, bi, respectively. The i-th clothes with ri, gi, and bi is defined as a point (ri, gi, bi) 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.

입력

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 ri, gi, bi (0 ≤ ri, gi, bi ≤ 1,000).

출력

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

예제 입력 1

2 1
36 16 85
74 87 38

예제 출력 1

4347.000000

예제 입력 2

1 2
12 26 90

예제 출력 2

0.000000

예제 입력 3

3 2
93 50 26
40 0 77
99 10 29

예제 출력 3

822.500000