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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

// ordtools {{{
#[allow(dead_code)]
mod ordtools {
    pub trait Ordtools: PartialOrd + Clone + Sized {
        fn change_min(&mut self, rhs: &Self) {
            if rhs < self {
                *self = rhs.clone();
            }
        }

        fn change_max(&mut self, rhs: &Self) {
            if rhs > self {
                *self = rhs.clone();
            }
        }
    }

    impl<T: PartialOrd + Clone + Sized> Ordtools for T {}
}
// }}}
use ordtools::Ordtools;

fn main() {
    input!(
        n: usize,
        clim: usize,
        d: [[u32; clim]; clim],
        c: [[proconio::marker::Usize1; n]; n]
    );
    let mut a = [0; 3];
    let mut cnt = vec![[0; 3]; clim];
    for i in 0..n {
        for j in 0..n {
            cnt[c[i][j]][(i + j) % 3] += 1;
        }
    }
    let mut ans = std::u32::MAX;
    loop {
        if a[0] != a[1] && a[1] != a[2] && a[2] != a[0] {
            let mut now = 0;
            for k in 0..clim {
                for l in 0..3 {
                    now += d[k][a[l]] * cnt[k][l];
                }
            }
            ans.change_min(&now);
        }

        if let Some(s) = (0..3).rfind(|&s| a[s] != clim - 1) {
            a[s] += 1;
            a[s + 1..].iter_mut().for_each(|x| *x = 0);
        } else {
            break;
        }
    }
    println!("{}", ans);
}