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