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.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

using System.Collections;

class Program
{
    static void Main()
    {



        int[] nc = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        int N = nc[0];
        int C = nc[1];

        int[,] D = new int[C, C];
        {
            for (int i = 0; i < C; i++)
            {
                int[] data = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

                for (int j = 0; j < C; j++)
                {
                    D[i, j] = data[j];
                }
                
            }
        }

        int[,] c = new int[N, N];
        {
            for (int i = 0; i < N; i++)
            {
                int[] data = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

                for(int j = 0; j < N; j++)
                {
                    c[i, j] = data[j] - 1;
                }
            }
        }

        //(i+j)%3がkであるマスを色cに変えたときの違和感の増分をX[k,c]とする。
        int[,] X = new int[3, C];
        for (int k = 0; k < 3; k++)
        {
            for (int cc = 0; cc < C; cc++)
            {
                int x = 0;

                for (int i = 0; i < N; i++)
                {
                    for (int j = 0; j < N; j++)
                    {
                        if ((i + j) % 3 == k)
                        {
                            x += D[c[i, j], cc];
                        }
                    }
                }
                X[k, cc] = x;
            }
        }

        int ans = int.MaxValue;

        //色の組み合わせ30*29*28の全部を試す
        for(int i = 0; i < C; i++)
        {
            for(int j = 0; j < C; j++)
            {
                if (j == i) continue;

                for(int k = 0; k < C; k++)
                {
                    if (k == j) continue;
                    if (k == i) continue;

                    ans = Math.Min(ans, X[0, i] + X[1, j] + X[2, k]);
                }
            }
        }

        Console.WriteLine(ans);
    }

    static bool isOkini(long N, long num)
    {
        if (num == 0) return false;

        long a = N % num;
        long b = N / num;

        if (a == b) return true;
        else return false;
    }
}


static class MathUtil
{
    public static IEnumerable<IEnumerable<int>> GetPermutation(int n)
    {
        if (n == 0)
        {
            yield return Single(0);
            yield break;
        }

        for (int i = 0; i <= n; i++)
        {
            foreach (var x in GetPermutation(n - 1))
            {
                yield return Single(i).Concat(x.Select(itm => itm < i ? itm : itm + 1));
            }
        }
    }

    private static IEnumerable<int> Single(int x)
    {
        yield return x;
    }

    public static IEnumerable<int> EnumeratePrimeNumbers()
    {
        List<int> primes = new List<int>() { 2 };
        yield return 2;

        for (int i = 3; i < int.MaxValue; i++)
        {
            bool isPrime = true;
            int Sqrt = (int)Math.Sqrt(i) + 1;

            foreach (var prime in primes)
            {
                if (prime > Sqrt)
                {
                    break;
                }
                if (i % prime == 0)
                {
                    isPrime = false;
                    break;
                }
            }

            if (isPrime)
            {
                primes.Add(i);
                yield return i;
            }
        }
    }
}