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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.D_Challenge
{
    class ABC_099
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nc = ReadInts();
            int n = nc[0];
            int c = nc[1];
            var ds = new int[c, c];
            for (int i = 0; i < c; i++)
            {
                int[] input = ReadInts();
                for(int j = 0; j < c; j++)
                {
                    ds[i, j] = input[j];
                }
            }

            var cs = new int[n, n];
            for (int i = 0; i < n; i++)
            {
                int[] input = ReadInts();
                for (int j = 0; j < n; j++)
                {
                    cs[i, j] = input[j];
                }
            }

            var colors = new int[3,c];//余りと色の個数
            for(int i = 0; i < n; i++)
            {
                for(int j = 0; j < n; j++)
                {
                    colors[(i + j) % 3, cs[i, j] - 1]++;
                }
            }

            var errors = new int[3][][];//違和感値初期化および計算
            for(int i = 0; i < 3; i++)
            {
                errors[i] = new int[c][];
                for(int j = 0; j < c; j++)
                {
                    errors[i][j] = new int[2];
                    errors[i][j][0] = j;
                    errors[i][j][1] = 0;
                    for(int k = 0; k < c; k++)
                    {//色kから色jに変えるときの違和感を加算
                        errors[i][j][1] += colors[i, k] * ds[k, j];
                    }
                }
            }
            Array.Sort(errors[0], (a, b) => a[1] - b[1]);
            Array.Sort(errors[1], (a, b) => a[1] - b[1]);
            Array.Sort(errors[2], (a, b) => a[1] - b[1]);
            int minErrorSum = int.MaxValue;
            for(int i = 0; i < 3; i++)
            {
                for (int j = 0; j < 3; j++)
                {

                    for (int k = 0; k < 3; k++)
                    {
                        if(errors[0][i][0]==errors[1][j][0]
                            || errors[1][j][0] == errors[2][k][0]
                            || errors[2][k][0] == errors[0][i][0])
                        {
                            continue;
                        }
                        else
                        {
                            int errorSum = errors[0][i][1]
                                + errors[1][j][1]
                                + errors[2][k][1];
                            minErrorSum = Math.Min(minErrorSum, errorSum);
                        }
                    }
                }
            }

            Console.WriteLine(minErrorSum);
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}