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.Linq;
using System.Linq.Expressions;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, CC;
        public int[,] D;
        public int[,] C;

        public void Run()
        {
            // input
            {
                var line = Input.ReadIntArray();
                N = line[0];
                CC = line[1];
                D = new int[CC, CC];
                C = new int[N, N];
            }

            for (int cfrom = 0; cfrom < CC; cfrom++)
            {
                var line = Input.ReadIntArray();
                for (int cto = 0; cto < CC; cto++)
                    D[cfrom, cto] = line[cto];
            }

            for (int y = 0; y < N; y++)
            {
                var line = Input.ReadIntArray();
                for (int x = 0; x < N; x++)
                    C[y, x] = line[x] - 1;
            }

            // Run
            var S = new long[CC, 3];
            for (int c = 0; c < CC; c++)
            for (int m = 0; m < 3; m++)
            {
                long s = 0;
                for (int y = 0; y < N; y++)
                for (int x = 0; x < N; x++)
                    if ((y + x) % 3 == m)
                        s += D[C[y, x], c];

                S[c, m] = s;
            }

            long ret = long.MaxValue;
            for (int c1 = 0; c1 < CC; c1++)
            for (int c2 = 0; c2 < CC; c2++)
            for (int c3 = 0; c3 < CC; c3++)
            {
                if (c1 == c2 || c1 == c3 || c2 == c3) continue;
                long r = S[c1, 0] + S[c2, 1] + S[c3, 2];
                ret = Math.Min(ret, r);
            }
            
            Console.WriteLine(ret);

        }
    }

    // libs ----------
    

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}