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 Rust (1.15.1) (judge verdict: Accepted)

// AtCoder My Practice
// author: Leonardone @ NEETSDKASU

fn main() {
	let mut stdin = String::new();
    std::io::Read::read_to_string(
    	&mut std::io::stdin(),
        &mut stdin).unwrap();
	let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
    	($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    let n = get!(usize);
    let c = get!(usize);
    let mut d = vec![vec![0; c+1]; c+1];
    for i in 1..c+1 {
    	for j in 1..c+1 {
        	d[i][j] = get!();
        }
    }
    let mut g = vec![vec![0i64; c+1]; 3];
    for i in 1..n+1 {
    	for j in 1..n+1 {
        	let p = (i + j) % 3;
            let c = get!(usize);
        	g[p][c] += 1;
        }
    }
    let mut ans = std::i64::MAX;
    for c0 in 1..c+1 {
    	let mut d0 = 0;
        for i in 0..g[0].len() {
        	d0 += g[0][i] * d[i][c0];
        }
    	for c1 in 1..c+1 {
        	if c0 == c1 {
            	continue;
            }
	    	let mut d1 = 0;
    	    for i in 0..g[1].len() {
        		d1 += g[1][i] * d[i][c1];
        	}
            for c2 in 1..c+1 {
            	if c0 == c2 || c1 == c2 {
                	continue;
                }
	    		let mut d2 = 0;
    	    	for i in 0..g[2].len() {
        			d2 += g[2][i] * d[i][c2];
        		}
                let d = d0+d1+d2;
                ans = std::cmp::min(ans, d);
            }
        }
    }
    println!("{}", ans);
}