4394 : Washer
- 제한시간
- 1000 ms
- 메모리제한
- 512 MB
- 해결횟수
- 2 회
- 시도횟수
- 24 회
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

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.
입력형식
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).
출력형식
Your program is to write to standard output. Print exactly one line containing the minimum total color transfer, rounded to the sixth decimal point.
입력 예복사하기 2 1 36 16 85 74 87 38 |
출력 예복사하기 4347.000000 |
입력 예복사하기 1 2 12 26 90 |
출력 예복사하기 0.000000 |
입력 예복사하기 3 2 93 50 26 40 0 77 99 10 29 |
출력 예복사하기 822.500000 |