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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cassert>
#include <iostream>
#include <sstream>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <utility>
#include <numeric>
#include <algorithm>
#include <bitset>
#include <complex>
#include <array>
#include <list>
#include <stack>
#include <valarray>

using namespace std;

int main(){
  int N,C;
  cin >> N >> C;
  int c[N][N];
  vector<vector<int>> t(3,vector<int>(C,0));
  int D[C][C];
  vector<int> MOD(C,0);

  for(int i = 0; i < C; i++) for(int j = 0; j < C; j++) cin >> D[i][j];
  for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) {
    cin >> c[i][j];
    t[(i+j)%3][c[i][j]-1] ++;
  }

  long ans = 1e15;
  for(int i = 0; i < C; i++){
    for(int j = 0; j < C; j++){
      if(i==j) continue;
      for(int k = 0; k < C; k++){
        if(i==k || j==k) continue;
        int cnt = 0;
        for(int l = 0;l < C; l++) cnt += D[l][i] * t[0][l];
        for(int l = 0;l < C; l++) cnt += D[l][j] * t[1][l];
        for(int l = 0;l < C; l++) cnt += D[l][k] * t[2][l];
        ans = min(ans,(long)cnt);
      }
    }
  }
  cout << ans << endl;
  
  return 0;
}