Problem:
Score : 400 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i,j) be the square at the i-th row from the top and the j-th column from the left.

These squares have to be painted in one of the C colors from Color 1 to Color C. Initially, (i,j) is painted in Color c_{i,j}.

We say the grid is a good grid when the following condition is met for all i,j,x,y satisfying 1 \leq i,j,x,y \leq N:

If (i+j) \% 3=(x+y) \% 3, the color of (i,j) and the color of (x,y) are the same.

If (i+j) \% 3 \neq (x+y) \% 3, the color of (i,j) and the color of (x,y) are different.

Here, X \% Y represents X modulo Y.

We will repaint zero or more squares so that the grid will be a good grid.

For a square, the wrongness when the color of the square is X before repainting and Y after repainting, is D_{X,Y}.

Find the minimum possible sum of the wrongness of all the squares.

Constraints

1 \leq N \leq 500

3 \leq C \leq 30

1 \leq D_{i,j} \leq 1000 (i \neq j),D_{i,j}=0 (i=j)

1 \leq c_{i,j} \leq C

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N C
D_{1,1} ... D_{1,C}
:
D_{C,1} ... D_{C,C}
c_{1,1} ... c_{1,N}
:
c_{N,1} ... c_{N,N}

Output

If the minimum possible sum of the wrongness of all the squares is x, print x.

Sample Input 1

2 3
0 1 1
1 0 1
1 4 0
1 2
3 3

Sample Output 1

3

Repaint (1,1) to Color 2. The wrongness of (1,1) becomes D_{1,2}=1.

Repaint (1,2) to Color 3. The wrongness of (1,2) becomes D_{2,3}=1.

Repaint (2,2) to Color 1. The wrongness of (2,2) becomes D_{3,1}=1.

In this case, the sum of the wrongness of all the squares is 3.

Note that D_{i,j} \neq D_{j,i} is possible.

Sample Input 2

4 3
0 12 71
81 0 53
14 92 0
1 1 2 1
2 1 1 2
2 2 1 3
1 1 2 2

Sample Output 2

428

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
		long n = long.Parse(input[0]);
		long c = long.Parse(input[1]);
    long answer = long.MaxValue;
    long answerMemo = 0;
    
    int[,] matrixDistance = new int[c,c];//行列
    for(int i = 0; i < c; i++)//それぞれの行
    {
    	int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
    	for(int j = 0; j < c; j++) matrixDistance[i,j] = nums[j];//行の全ての成分
    }

    int[,] matrixColor = new int[n,n];//行列  
    for(int i = 0; i < n; i++)//それぞれの行
    {
    	int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
    	for(int j = 0; j < n; j++) matrixColor[i,j] = nums[j];//行の全ての成分
    }

    for(int i = 0; i < c; i++)//全色試す
    {
      for(int j = 0; j < c; j++)
      {
        for(int k = 0; k < c; k++)
        {
          if(i == j || i == k || j == k) continue;//同じ色はダメ
          answerMemo = 0;

          for(int a = 0; a < n; a++)
          {
            for(int b = 0; b < n; b++)
            {
              if((a+b)% 3 == 0)
                answerMemo += matrixDistance[matrixColor[a,b]-1, i];
              if((a+b)% 3 == 1)
                answerMemo += matrixDistance[matrixColor[a,b]-1, j];
              if((a+b)% 3 == 2)
                answerMemo += matrixDistance[matrixColor[a,b]-1, k];
            }
          }

          answer = Math.Min(answer, answerMemo);
          
        }
      }
    }

    
		Console.WriteLine(answer);
	}
}