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)

use std::io::prelude::*;

fn input<T: std::str::FromStr>() -> T {
    let stdin = std::io::stdin();
    let it = stdin.lock().bytes().map(|c| c.unwrap() as char);
    let (fs, ft) = (|c: &char| c.is_whitespace(), |c: &char| !c.is_whitespace());
    let token = it.skip_while(fs).take_while(ft).collect::<String>();
    token.parse().ok().unwrap()
}
#[allow(dead_code)]
fn with_stdout_lock<F: FnOnce(std::io::BufWriter<std::io::StdoutLock>)>(f: F) {
    let out = std::io::stdout();
    f(std::io::BufWriter::new(out.lock()));
}
#[allow(unused_macros)]
macro_rules! debug {
    ($($var:expr),*) => { #[cfg(debug_assertions)] {
        $({ match &$var { v => eprint!("{}={:?} ", stringify!($var), v) } })*
        eprintln!();
    }};
}

fn main() {
    let n: usize = input();
    let nc: usize = input();
    let d: Vec<Vec<usize>> = (0..nc)
        .map(|_| (0..nc).map(|_| input()).collect())
        .collect();
    let c: Vec<Vec<usize>> = (0..n).map(|_| (0..n).map(|_| input()).collect()).collect();

    let mut color = vec![vec![0; nc]; 3];
    for i in 0..n {
        for j in 0..n {
            color[(i + j) % 3][c[i][j] - 1] += 1;
        }
    }

    let mut cost = vec![vec![0; nc]; 3];
    for i in 0..3 {
        for col in 0..nc {
            for x in 0..nc {
                cost[i][col] += color[i][x] * d[x][col];
            }
        }
    }

    let mut ans = usize::max_value();
    for i in 0..nc {
        for j in 0..nc {
            if i == j {
                continue;
            }
            for k in 0..nc {
                if i == k || j == k {
                    continue;
                }
                ans = std::cmp::min(ans, cost[0][i] + cost[1][j] + cost[2][k]);
            }
        }
    }

    println!("{}", ans);
}