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;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var nc = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int n = nc[0];
			int c = nc[1];

			int[,] d = new int[c, c];
			for (int i = 0; i < c; i++) {
				var ds = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				for (int j = 0; j < c; j++) {
					d[i, j] = ds[j];
				}
			}

			int[,] colors = new int[n, n];
			for (int i = 0; i < n; i++) {
				var cs = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				for (int j = 0; j < n; j++) {
					colors[i, j] = cs[j] - 1;
				}
			}

			int[,] sumD = new int[3, c];
			for (int i = 0; i < c; i++) {
				for (int ii = 0; ii < n; ii++) {
					for (int jj = 0; jj < n; jj++) {
						int p = (ii + jj) % 3;
						sumD[p, i] += d[colors[ii, jj], i];
					}
				}
			}

			int ans = int.MaxValue;
			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 (k == i || k == j) {
							continue;
						}

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

			Console.WriteLine(ans);
		}
	}
}