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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main
{

  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);
    String[] sl = r.readLine().split("[\\s]+");
    int n = Integer.parseInt(sl[0]);
    int c = Integer.parseInt(sl[1]);
    int d[][] = new int[30][30];
    int count[][] = new int[3][30];

    for(int i = 0; i < c; i++)
    {
      sl = r.readLine().split("[\\s]+");
      for(int j = 0; j < c; j++)
      {
        d[i][j] = Integer.parseInt(sl[j]);
      }
    }

    for(int i = 0; i < n; i++)
    {
      sl = r.readLine().split("[\\s]+");
      for(int j = 0; j < n; j++)
      {
        count[(i + j) % 3][Integer.parseInt(sl[j]) - 1]++;
      }
    }
    
    int sel[] = new int[3];
    int min = Integer.MAX_VALUE;
    
    for(sel[0] = 0; sel[0] < c; sel[0]++)
    {
      for(sel[1] = 0; sel[1] < c; sel[1]++)
      {
        if(sel[0] == sel[1])
        {
          continue;
        }
        for(sel[2] = 0; sel[2] < c; sel[2]++)
        {
          if(sel[1] == sel[2] || sel[0] == sel[2])
          {
            continue;
          }
          
          int stress = 0;
          for(int i = 0; i < 3; i++)
          {
            for(int j = 0; j < c; j++)
            {
              stress += count[i][j] * d[j][sel[i]];
            }
          }
          min = Math.min(min, stress);
        }
      }
    }
    
    System.out.println(min);

  }


}