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;
using System.Collections.Generic;
using System.Text;


public class Pair
{
	public int Color { get; private set; }
	public int Strange { get; private set; }

	public Pair(int color, int strange)
	{
		Color = color;
		Strange = strange;
	}
}


public class D
{
	public static void Main()
	{
		string[] args;

		args = Console.ReadLine().Split(' ');
		int N = Int32.Parse(args[0]);
		int C = Int32.Parse(args[1]);

		int[,] D = new int[C,C];
		for(int i = 0; i < C; i++)
		{
			args = Console.ReadLine().Split(' ');
			for(int j = 0; j < C; j++)
				D[i,j] = Int32.Parse(args[j]);
		}

		int[,] c = new int[N,N];
		for(int i = 0; i < N; i++)
		{
			args = Console.ReadLine().Split(' ');
			for(int j = 0; j < N; j++)
				c[i,j] = Int32.Parse(args[j]) - 1;
		}
		
		List<List<Pair>> lists = new List<List<Pair>>(3);
		for(int i = 0; i < 3; i++)
			lists.Add(new List<Pair>(N));

		for(int k = 0; k < C; k++)
		{
			int[] sum = new int[3];
			for(int i = 0; i < N; i++)
				for(int j = 0; j < N; j++)
					sum[(i + j) % 3] += D[c[i,j],k];

			for(int i = 0; i < 3; i++)
				lists[i].Add(new Pair(k, sum[i]));
		}

		for(int i = 0; i < 3; i++)
			lists[i].Sort((x,y) => x.Strange - y.Strange);

		int ans = Int32.MaxValue;
		for(int mask = 0; mask < 27; mask++)
		{
			int tmp = mask;
			int[] rank = new int[3];
			for(int i = 0; i < 3; i++)
			{
				rank[i] = tmp % 3;
				tmp /= 3;
			}

			if(lists[0][rank[0]].Color == lists[1][rank[1]].Color ||
				lists[1][rank[1]].Color == lists[2][rank[2]].Color ||
				lists[2][rank[2]].Color == lists[0][rank[0]].Color )
				continue;

			int sum = 
				lists[0][rank[0]].Strange + 
				lists[1][rank[1]].Strange + 
				lists[2][rank[2]].Strange;
			ans = Math.Min(ans,sum);
		}

		Console.WriteLine(ans);		
	}	
}