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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
 
public class Main{
	public static void main(String[] args){
    	Scanner sc = new Scanner(System.in);
      	int n = sc.nextInt();
      	int c_num = sc.nextInt();
      	int[][] d = new int[c_num][c_num];
      	int[][] c = new int[n][n];

      	for(int i = 0 ; i < c_num ; i++){
      		for(int j = 0 ; j < c_num ; j++){
      			d[i][j] = sc.nextInt();
      		}
      	}
      	for(int i = 0 ; i < n ; i++){
      		for(int j = 0 ; j < n ; j++){
      			c[i][j] = sc.nextInt()-1;
      		}
      	}

      	int min = (int)1e9;
      	int[] color = new int[3];
      	int[] swap23 = { 0, 2, 1};
      	for(color[0] = 0 ; color[0] < c_num-2 ; color[0]++){
      		for(color[1] = color[0]+1 ; color[1] < c_num-1 ; color[1]++){
      			for(color[2] = color[1]+1 ; color[2] < c_num ; color[2]++){
      				for(int k = 0 ; k < 3 ; k++){
      					int iwa = 0;
	      				for(int i = 0 ; i < n ; i++){
	      					for(int j = 0 ; j < n ; j++){
	      						iwa += d[c[i][j]][color[(i+j+k)%3]];
	      					}
	      				}
      					min = Math.min(iwa, min);

      					iwa = 0;
	      				for(int i = 0 ; i < n ; i++){
	      					for(int j = 0 ; j < n ; j++){
	      						iwa += d[c[i][j]][color[swap23[(i+j+k)%3]]];
	      					}
	      				}
      					min = Math.min(iwa, min);
      				}
      			}
      		}
      	}

      	System.out.println(min);
    }
}