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.io.File;
import java.io.IOException;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;
import java.util.Map.Entry;

public class Main {
	
	public static void main(String[] args) throws IOException {
		//File file = new File("input.txt");
		//Scanner in = new Scanner(file);
		
		Scanner in = new Scanner(System.in);

		int N = in.nextInt();
		int C = in.nextInt();
		int[][] D = new int[C][C];
		long[][] d = new long[3][C];
		
		for(int i = 0; i < C; i++){
			for(int j = 0; j < C; j++) D[i][j] = in.nextInt();
		}
		
		int[][] c = new int[N][N];
		for(int i = 0; i < N; i++){
			for(int j = 0; j < N; j++){
				c[i][j] = in.nextInt();
				for(int k = 1; k <= C; k++){
					d[((i + j) % 3)][k-1] += D[c[i][j]-1][k-1];
				}
			}
		}
		
		long min = Long.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;
					long cost = 0;
					cost += d[0][i-1];
					cost += d[1][j-1];
					cost += d[2][k-1];
					min = Math.min(min, cost);
				}
			}
		}
		
		System.out.println(min);
	}
}