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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

	import java.util.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 static List<ArrayList<Integer>> list= new ArrayList<ArrayList<Integer>>();
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();
	        int C = sc.nextInt();
	        int[][] D = new int[C][C];
	        for(int i=0;i<C;i++) {
	        	for(int j=0;j<C;j++) {
	        		D[i][j]=sc.nextInt();
	        	}
	        }
	        int[][] c = new int[N][N];
	        int[] m1 = new int[N*N];
	        int[] m2 = new int[N*N];
	        int[] m3 = new int[N*N];
	        int cnt1 =0;
	        int cnt2 =0;
	        int cnt3 =0;
	        for(int i=0;i<N;i++) {
	        	for(int j=0;j<N;j++) {
	        		c[i][j]=sc.nextInt()-1;
	        		int t = i+j;
	        		if(t%3==0) {
	        			m1[cnt1]=c[i][j];
	        			cnt1++;
	        		}
	        		if(t%3==1) {
	        			m2[cnt2]=c[i][j];
	        			cnt2++;
	        		}
	        		if(t%3==2) {
	        			m3[cnt3]=c[i][j];
	        			cnt3++;
	        		}
	        	}
	        }
	        
	        long ans=Long.MAX_VALUE;
	        boolean flg =false;
	        int[] d = new int[3];
	        while(d[0]<=C-1) {	        	
	        	if(d[0]==d[1])flg=true;
	        	if(d[1]==d[2])flg=true;
	        	if(d[0]==d[2])flg=true;
	        	long sum =0;
	        	if(flg==false) {
		        	for(int i=0;i<N;i++) {
		        		for(int j=0;j<N;j++) {
		        			int t = i+j;
		        			if(t%3==0) {
		        				sum=sum+D[c[i][j]][d[0]];
		        			}
		        			if(t%3==1) {
		        				sum=sum+D[c[i][j]][d[1]];
		        			}
		        			if(t%3==2) {
		        				sum=sum+D[c[i][j]][d[2]];
		        			}
		        		}
		        	}	        		
		        	ans=Math.min(ans,sum);
	        	}

	        	
	        	d[2]++;
	        	if(d[2]>=C) {
	        		d[1]++;
	        		d[2]=0;
	        		if(d[1]>=C) {
	        			d[0]++;
	        			d[1]=0;
	        		}
	        	}
	        	flg=false;
	        }
	        
	        
	        
	        System.out.println(ans);
		 }
		 
	 
	}