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.IO;
using System.Runtime.InteropServices;
using System.Runtime.Remoting.Contexts;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;

        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }

            var res = line[index];
            index++;
            return res;
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }

        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }

        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }
    }

    class Program
    {
        private int N;
        private int C;
        private int[][] D;
        private int[][] c;
        private int[,] change;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
            C = sc.NextInt();
            D = new int[C][];
            for (int i = 0; i < C; i++)
            {
                D[i] = sc.IntArray();
            }

            c = new int[N][];
            for (int i = 0; i < N; i++)
            {
                c[i] = sc.IntArray().Select(j => j - 1).ToArray();
            }
        }


        public void Solve()
        {
            Scan();
            int ans = int.MaxValue;
            change = new int[3, C];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    int index = (i + j) % 3;
                    for (int k = 0; k < C; k++)
                    {
                        change[index, k] += D[c[i][j]][k];
                    }
                }
            }
            for (int i = 0; i < C; i++)
            {
                for (int j = 0; j < C; j++)
                {
                    if (i == j) continue;
                    for (int k = 0; k < C; k++)
                    {
                        if (i == k || j == k) continue;
                        ans = Math.Min(ans, Calc(i, j, k));
                    }
                }
            }
            Console.WriteLine(ans);
        }

        private int Calc(params int[] col)
        {
            return change[0, col[0]] + change[1, col[1]] + change[2, col[2]];
        }


        static void Main() => new Program().Solve();
    }

}