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;
class Program{
	static int[] s,f=new int[3];
	static bool[] b;
	static long ans=long.MaxValue;
	static long[,] h;
	static void Main(){
		s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		h=new long[3,s[1]+1];
		long[][] arr=new long[s[1]+1][];
		for(int i=1;i<=s[1];i++){
			arr[i]=Array.ConvertAll(("0 "+Console.ReadLine()).Split(),long.Parse);
		}
		for(int i=0;i<s[0];i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			for(int j=0;j<s[0];j++){
				for(int k=1;k<=s[1];k++){
					h[(i+j)%3,k]+=arr[q[j]][k];
				}
			}
		}
		b=new bool[s[1]];
		fu1(0);
		Console.WriteLine("{0}",ans);
	}
	static void fu1(int a){
		for(int i=0;i<s[1];i++){
			if(!b[i]){
				f[a]=i+1;
				if(a==2){
					long o=h[0,f[0]]+h[1,f[1]]+h[2,f[2]];
					ans=Math.Min(ans,o);
				}
				else{
					b[i]=true;
					fu1(a+1);
					b[i]=false;
				}
			}
		}
	}
}