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.*;
import java.util.Map.Entry;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int C = Integer.parseInt(sc.next());
        int[][] D = new int[C][C];
        int[][] c = new int[N][N];
        for (int i=0;i<C;i++) {
            for (int j=0;j<C;j++) {
                D[i][j] = Integer.parseInt(sc.next());
            }
        }
        for (int i=0;i<N;i++) {
            for (int j=0;j<N;j++) {
                c[i][j] = Integer.parseInt(sc.next());
            }
        }

        ArrayList<HashMap<Integer, Integer>> map_list = new ArrayList<HashMap<Integer, Integer>>();
        for (int i=0;i<3;i++) {
            HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
            for (int j=0;j<N;j++) {
                for (int k=0;k<N;k++) {
                    if ((j+k)%3==i) {
                        if (!map.containsKey(c[j][k])) {
                            map.put(c[j][k], 1);
                        } else {
                            map.put(c[j][k], map.get(c[j][k])+1);
                        }
                    }
                }
            }
            map_list.add(map);
        }

        long ans = Integer.MAX_VALUE;
        for (int i=0;i<C;i++) {
            for (int j=0;j<C;j++) {
                for (int k=0;k<C;k++) {
                    if (i==j || i==k || j==k) {
                        continue;
                    }
                    // System.out.println("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA");
                    long tmp = 0L;
                    for (int l=0;l<3;l++) {
                        for (Entry<Integer, Integer> entry : map_list.get(l).entrySet()) {
                            int key = entry.getKey();
                            int value = entry.getValue();
                            // System.out.println(entry.getKey() + " " + entry.getValue());
                            int index;
                            if (l==0) {
                                index = i;
                            } else if (l==1) {
                                index = j;
                            } else {
                                index = k;
                            }
                            tmp += value*D[key-1][index];
                            // System.out.println("value index key-1 " + value + " " + index + " " + (key-1));
                        }
                    }
                    ans = Math.min(ans, tmp);
                }
            }
        }
        // System.out.println(map_list);
        System.out.println(ans);
    }
}