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
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <string>
#include <cstring>
#include <ctime>
#include <climits>
#include <limits>

using namespace std;

//conversion
//------------------------------------------
inline int toInt(string s) { int v; istringstream sin(s); sin >> v; return v; }
template<class T> inline string toString(T x) { ostringstream sout; sout << x; return sout.str(); }

//math
//-------------------------------------------
template<class T> inline T sqr(T x) { return x * x; }

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define EXISTch(s,c) ((((s).find_first_of(c)) != std::string::npos)? 1 : 0)//cがあれば1 if(1)
#define SORT(c) sort((c).begin(),(c).end())

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int INF = (int)1000000007;
const LL MOD = (LL)1000000007;//10^9+7
const LL INF2 = (LL)100000000000000000;//10^18

int main() {
	int n, c; cin >> n >> c;

	vector<vector<int>> d(c, vector<int>(c));
	for (int i = 0; i < c; i++) {
		for (int j = 0; j < c; j++) {
			cin >> d[i][j];
		}
	}

	vector<vector<int>> a(n, vector<int>(n));
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cin >> a[i][j];
			--a[i][j];
		}
	}

	//塗り替える先の色を決めて、集める
	//a[j][k]を決めた色にするのはd[a[j][k]][i]
	//全てのaの要素について、(i+j)%3で分類して集める

	vector<vector<int>> cost(3, vector<int>(c));
	for (int i = 0; i < c; i++) {
		for (int j = 0; j < n; j++) {
			for (int k = 0; k < n; k++) {
				cost[(j+k) % 3][i] += d[a[j][k]][i];
			}
		}
	}

	int res = INF;

	//(i+j)%3の余り0,1,2の類に対して
	//色の割当てを全探索

	for (int c1 = 0; c1 < c; c1++) {
		for (int c2 = 0; c2 < c; c2++) {
			for (int c3 = 0; c3 < c; c3++) {
				if (c1==c2 || c2==c3||c1==c3)continue;
				int cnt = 0;

				cnt += cost[0][c1];
				cnt += cost[1][c2];
				cnt += cost[2][c3];

				res = min(res, cnt);
			}

		}

	}

	cout << res << endl;

	return 0;
}