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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)


import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);

		int N = scanner.nextInt();
		int C = scanner.nextInt();

		int[][] D = new int[C][C];

		ArrayList<Integer> Cmod0 = new ArrayList<>();
		ArrayList<Integer> Cmod1 = new ArrayList<>();
		ArrayList<Integer> Cmod2 = new ArrayList<>();

		for(int i = 0;i < C; i++) {
			for (int j = 0; j < C; j++) {
				D[i][j]=scanner.nextInt();
			}
		}

		for(int i = 1;i <= N; i++) {
			for (int j = 1; j <= N; j++) {
				if((i+j)%3 == 0) {
					Cmod0.add(scanner.nextInt());
				}else if((i+j)%3 == 1) {
					Cmod1.add(scanner.nextInt());
				}else if((i+j)%3 == 2) {
					Cmod2.add(scanner.nextInt());
				}
			}
		}

		int min=Integer.MAX_VALUE;
		int min_temp = 0;
		for (int i = 0; i < C; i++) {
			for (int j = 0; j < C ; j++) {
				if(i==j)continue;
				for (int j2 = 0; j2 < C ; j2++) {
					if(j2 == i || j2 == j)continue;
					for (int k = 0; k < Cmod0.size(); k++) {
						min_temp += D[Cmod0.get(k)-1][i];
					}
					for (int k = 0; k < Cmod1.size(); k++) {
						min_temp += D[Cmod1.get(k)-1][j];
					}
					for (int k = 0; k < Cmod2.size(); k++) {
						min_temp += D[Cmod2.get(k)-1][j2];
					}

					min = (min>min_temp)?min_temp:min;
					min_temp = 0;
				}

			}

		}

		System.out.println(min);


	}

}