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.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int c = sc.nextInt();
		int[][] matrix = new int[c + 1][c + 1];
		for (int i = 1; i <= c; i++) {
		    for (int j = 1; j <= c; j++) {
		        matrix[i][j] = sc.nextInt();
		    }
		}
		int[][] costs = new int[3][c + 1];
		for (int i = 1; i <= n; i++) {
		    for (int j = 1; j <= n; j++) {
		        int type = (i + j) % 3;
		        int color = sc.nextInt();
		        for (int k = 1; k <= c; k++) {
		            costs[type][k] += matrix[color][k];
		        }
		    }
		}
		int min = Integer.MAX_VALUE;
		for (int i = 1; i <= c; i++) {
		    for (int j = 1; j <= c; j++) {
		        if (i == j) {
		            continue;
		        }
		        for (int k = 1; k <= c; k++) {
		            if (i == k || j == k) {
		                continue;
		            }
		            min = Math.min(min, costs[0][i] + costs[1][j] + costs[2][k]);
		        }
		    }
		}
		System.out.println(min);
    }
}