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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static StreamReader sr;

        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)998244353;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NC = Sarray();
            var N = NC[0];
            var C = NC[1];

            var Di = new long[C][];
            for (var i = 0; i < C; ++i)
                Di[i] = Sarray();
            // 色をiからjに変更するときの違和感の最小値
            /*for (var k = 0; k < C; ++k)
                for (var i = 0; i < C; ++i)
                    for (var j = 0; j < C; ++j)
                        Di[i][j] = Min(Di[i][j], Di[i][k] + Di[k][j]);*/

            var Ci = Enumerable.Range(0, 3).Select(_ => new long[C]).ToArray();
            // %3のグリッドについて出てくる色の数
            for (var i = 0; i < N; ++i)
            {
                var cij = Sarray();
                for (var j = 0; j < N; ++j)
                    ++Ci[(i + j) % 3][cij[j] - 1];
            }

            // 色を3つ決めて違和感を計算
            var ans = long.MaxValue;
            for (var i = 0; i < C; ++i)
            {
                for (var j = 0; j < C; ++j)
                {
                    if (i == j) continue;
                    for (var k = 0; k < C; ++k)
                    {
                        if (j == k || i == k) continue;
                        var t = 0L;
                        for (var l = 0; l < C; ++l)
                        {
                            t += Di[l][i] * Ci[0][l];
                            t += Di[l][j] * Ci[1][l];
                            t += Di[l][k] * Ci[2][l];
                        }
                        ans = Min(ans, t);
                    }
                }
            }
            WriteLine(ans);
            //Out.Flush();
        }
    }
}