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<bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;

const double PI = acos(-1);
const int inf = 2e9;
const ll INF = 2e18;
const ll MOD = 1e9+7;

#define sz(s) (s).size()
#define pb push_back
#define fi first
#define se second
#define REP(i,n) for (int i = 0; i<n; i++)
#define ALL(a) begin(a), end(a)

int main (void) {
  int N,C;
  cin>>N>>C;
  vector<vector<int>> D(C,vector<int>(C));
  REP(i,C) {
    REP(j,C) {
      cin>>D[i][j];
    }
  }
  vector<vector<int>> G(N,vector<int>(N));
  REP(i,N) {
    REP(j,N) {
      cin>>G[i][j];
    }
  }

  vector<vector<int>> A(3,vector<int>(C,0));
  REP(i,N) {
    REP(j,N) {
      int n = (i + j) % 3;
      REP(k,C) {
        A[n][k] += D[G[i][j]-1][k];
      }
    }
  }

  ll ans = INF;
  REP(i,C) {
    REP(j,C) {
      REP(k,C) {
        if (i==j || j==k || k==i) continue;
        ll sum = A[0][i] + A[1][j] + A[2][k];
        ans = min(ans,sum);
      }
    }
  }
  cout<<ans<<endl;
  return 0;
}