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 $x$.