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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <cmath>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <functional>
#include <bitset>
#include <cassert>
#include <random>
using namespace std;
using ll = long long;



int main() {
	int N, C; cin >> N >> C;
	vector<vector<int>> cost(C + 2, vector<int>(C + 2));
	for (int i = 0; i < C; i++) {
		for (int j = 0; j < C; j++) {
			cin >> cost[i][j];
		}
	}
	vector<vector<int>> cnt(5, vector<int>(C + 2));
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < N; j++) {
			int c; cin >> c;
			cnt[(i + j) % 3][c - 1]++;
		}
	}

	int ans = 2e9;
	for (int a = 0; a < C; a++) {
		for (int b = 0; b < C; b++) {
			if (a == b) continue;
			for (int c = 0; c < C; c++) {
				if (a == c || b == c) continue;
				int s = 0;
				for (int i = 0; i < C; i++) {
					s += cost[i][a] * cnt[0][i];
					s += cost[i][b] * cnt[1][i];
					s += cost[i][c] * cnt[2][i];
				}
				ans = min(ans, s);
			}
		}
	}
	cout << ans << endl;
	return 0;
}