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;

namespace atcorder
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            atcorder.Good_Grid.Run();
        }
    }
    public class Good_Grid
    {
        public Good_Grid()
        {
        }
        public static void Run(){
            string s;
            int N, C;
            s = Console.ReadLine();
            N = int.Parse(s.Split(' ')[0]);
            C = int.Parse(s.Split(' ')[1]);
            int[,] D = new int[C, C];
            for (int i = 0; i < C;i++){
                s = Console.ReadLine();
                for (int j = 0; j < C;j++){
                    D[i, j] = int.Parse(s.Split(' ')[j]);
                }
            }
            int[,] c = new int[N, N];
            for (int i = 0; i < N; i++)
            {
                s = Console.ReadLine();
                for (int j = 0; j < N; j++)
                {
                    c[i, j] = int.Parse(s.Split(' ')[j])-1;
                }
            }

            //グループごとの色のカウント
            int[,] group = new int[3,C];
            for (int i = 0; i < N;i++){
                for (int j = 0; j < N;j++){
                    group[(i + j) % 3, c[i, j]]++;
                }
            }

            //塗り替えコストのワースト3をだす
            int[,] lowscore = new int[3, 3];
            for (int i = 0; i < 3; i++)
                for (int j = 0; j < 3; j++) lowscore[i, j] = int.MaxValue;
            int[,] color = new int[3, 3];
            for (int j = 0; j < C; j++)//色jに塗り替える
            {
                int[] sum=new int[3];
                for (int i = 0; i < C; i++)//色iから塗り替える
                {
                    sum[0] += D[i, j] * group[0, i];
                    sum[1] += D[i, j] * group[1, i];
                    sum[2] += D[i, j] * group[2, i];
                }
                for (int i = 0; i < 3;i++){
                    if(lowscore[i,0]>=sum[i]){
                        lowscore[i, 2] = lowscore[i, 1];
                        color[i, 2] = color[i, 1];
                        lowscore[i, 1] = lowscore[i, 0];
                        color[i, 1] = color[i, 0];
                        lowscore[i, 0] = sum[i];
                        color[i, 0] = j;
                    }else if(lowscore[i, 1] >= sum[i]){
                        lowscore[i, 2] = lowscore[i, 1];
                        color[i, 2] = color[i, 1];
                        lowscore[i, 1] = sum[i];
                        color[i, 1] = j;
                    }else if(lowscore[i, 2] >= sum[i]){
                        lowscore[i, 2] = sum[i];
                        color[i, 2] = j;
                    }
                }
            }

            //ワースト３から組み合わせで最少を求める
            int min = int.MaxValue;
            for (int i = 0; i < 3;i++){//0はワーストi
                for (int j = 0; j < 3;j++){//1はワーストj
                    for (int k = 0; k < 3;k++){//2はワーストkを選ぶ
                        if(color[0,i]!=color[1,j]&&color[0,i]!=color[2,k]&&color[1,j]!=color[2,k]){
                            int l = lowscore[0, i] + lowscore[1, j] + lowscore[2, k];
                            if (min > l) min = l;
                        }
                    }
                }
            }
            Console.WriteLine(min);
        }
    }
}