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: Time Limit Exceeded)

#include <bits/stdc++.h>
#include <cmath>

using namespace std;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
//#define rep(i, n) for (int i = 0; i < (n); ++i)
#define sz(x) ll(x.size())
typedef long long ll;
//typedef pair<int, int> P;
typedef pair<ll, ll> P;
//const double INF = 1e10;
const ll INF = 10e10;
const ll MINF = -10e10;
//const int INF = INT_MAX;
#define mins(x, y) x = min(x, y)
#define maxs(x, y) x = max(x, y)

typedef priority_queue<P, vector<P>, greater<P> > PQ_ASK;
const int mod = 1000000007;
//ifstream myfile("C:\\Users\\riku\\Downloads\\0_00.txt");
//ofstream outfile("log.txt");
//outfile << setw(6) << setfill('0') << prefecture << setw(6) << setfill('0') << rank << endl;
// std::cout << std::bitset<8>(9);

int main() {

// 普通に実装
// (i + j) % 3 = 0の色が0 ~ c

    int n, c;
    cin >> n >> c;


    vector<vector<int>> colors(n + 1, vector<int>(n + 1, 0));
    vector<vector<int>> iwakans(c, vector<int>(c, 0));

    rep(i, c) rep(j, c) {
            int d;
            cin >> d;
            iwakans[i][j] = d;
        }

    rep(x, n)rep(y, n) {
            int cc;
            cin >> cc;
            cc--;
            colors[x + 1][y + 1] = cc;
        }


    ll ans = INF;
    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;

//                printf("%d %d %d\n", i, j, k);

                ll now = 0;
//                if (i == 2 && j == 0 && k == 1) {
//                    cout << endl;
//                }

                for (int x = 1; x <= n; x++) {
                    for (int y = 1; y <= n; y++) {


                        int color = colors[x][y];
                        int h_color;
                        if ((x + y) % 3 == 0) {
                            h_color = i;
                        } else if ((x + y) % 3 == 1) {
                            h_color = j;
                        } else {
                            h_color = k;
                        }

                        if (color != h_color) {
                            now += iwakans[color][h_color];

//                            printf("%d %d wo %d kara %d cost %d\n", x, y, color, h_color, iwakans[color][h_color]);

                        }

                    }
                }
//                cout << now << endl;
                mins(ans, now);
            }
        }
    }

    cout << ans << endl;

}