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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Math;

class P
{
  static int[] Input(){
    return Console.ReadLine().Split().Select(int.Parse).ToArray();
  }

  static int[][] Input2(int n){
    int[][] X = new int[n][];
    for(int i = 0; i < n; i++){
      X[i] = Input();
    }
    return X;
  }

  static void Main()
  {
    int[] NC = Input();
    int[][] X = Input2(NC[1]); int[][] Y = Input2(NC[0]);
    int[,] Z = new int[3,NC[1]];
    for(int i = 0; i < NC[0]; i++){
      for(int j = 0; j < NC[0]; j++){
        for(int l = 0; l < NC[1]; l++){
          Z[(i+j)%3, l] += X[Y[i][j]-1][l];
        }
      }
    }
    int R = 2000000000;
    for(int i = 0; i < NC[1]; i++){
      for(int j = 0; j < NC[1]; j++){
        if (i==j)continue;
        for(int k = 0; k < NC[1]; k++){
          if (k==i^k==j)continue;
          R = Min(R, Z[0, i]+Z[1, j]+Z[2, k]);
        }
      }
    }
    Console.WriteLine(R);
  }
}