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: Accepted)

import java.util.Random;
import java.util.Scanner;

public class Main {
    public static int[][] cArray;
    public static int[][] dArray;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int c = sc.nextInt();
        cArray = new int[n][n];
        dArray = new int[c][c];
        for(int y = 0;y < c;++y){
            for (int x = 0;x < c;++x){
                dArray[x][y] = sc.nextInt();
            }
        }
        for(int y = 0;y < n;++y){
            for (int x = 0;x < n;++x){
                cArray[x][y] = sc.nextInt();
            }
        }
       // genre(n,c);
        search(n,c);
    }

    public static void genre(int n,int c){
        Random random = new Random();
        for(int y = 0;y < c;++y){
            for (int x = 0;x < c;++x){
                if(x == y)continue;
                dArray[x][y] = random.nextInt(1000);
            }
        }
        for(int y = 0;y < n;++y){
            for (int x = 0;x < n;++x){
                cArray[x][y] = random.nextInt(c) + 1;
            }
        }
    }

    public static void search(int n,int c){
        int cc[][] = new int[3][c];
        int s = 2;
        for (int x = 0;x < n;++x){
            s = (x + 2) % 3;
            for (int y = 0;y < n;++y){
                ++cc[s][cArray[x][y] - 1];
                ++s;
                if(s == 3)s = 0;
            }
        }

        long min = Long.MAX_VALUE;
        for (int c1 = 1;c1 <= c;++c1) {
            for (int c2 = 1; c2 <= c; ++c2) {
                if (c2 == c1) continue;
                for (int c3 = 1; c3 <= c; ++c3) {
                    if (c1 == c3 || c2 == c3) continue;
                    long k = 0;
                    for (int nn = 0;nn < c;++nn){
                        k += dArray[c3 - 1][nn] * cc[0][nn];
                        k += dArray[c1 - 1][nn] * cc[1][nn];
                        k += dArray[c2 - 1][nn] * cc[2][nn];
                    }
                    if(min > k)min = k;
                }
            }
        }


        System.out.println(min);
    }

}