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)

#![allow(non_snake_case)]

use std::io;
use std::str::FromStr;
use std::cmp::min;

macro_rules! parse_line {
    ($($t: ty),+) => ({
        let mut a_str = String::new();
        io::stdin().read_line(&mut a_str).expect("read error");
        let mut a_iter = a_str.split_whitespace();
        (
            $(
                a_iter.next().unwrap().parse::<$t>().expect("parse error"),
            )+
        )
    })
}

fn parse_line_to_vec<T: FromStr>() -> Vec<T> {
    let mut tmp = String::new();
    io::stdin().read_line(&mut tmp).expect("read error");
    return tmp.split_whitespace().filter_map(|s| T::from_str(s.trim()).ok()).collect();
}

fn main() {
    let (N, C) = parse_line!(usize, usize);
    let mut D = Vec::<Vec<u32>>::new();
    let mut c = Vec::<Vec<u32>>::new();
    for _ in 0..C {
        D.push(parse_line_to_vec());
    }
    for _ in 0..N {
        c.push(parse_line_to_vec());
    }

    let mut color_counts = Vec::new();
    for i in 0..3 {
        color_counts.push(Vec::new());
        color_counts[i].resize(C as usize, 0);
    }
    for i in 0..N {
        for j in 0..N {
            color_counts[((i + j) % 3) as usize][c[i][j] as usize - 1] += 1;
        }
    }

    let mut min_cost = u32::max_value();
    for c0 in 0..C {
        for c1 in 0..C {
            if c0 == c1 {
                continue;
            }
            for c2 in 0..C {
                if c0 == c2 || c1 == c2 {
                    continue;
                }
                let mut cost = 0u32;
                for j in 0..C {
                    cost += color_counts[0][j] * D[j][c0];
                    cost += color_counts[1][j] * D[j][c1];
                    cost += color_counts[2][j] * D[j][c2];
                }
                min_cost = min(min_cost, cost);
            }
        }
    }
    println!("{}", min_cost);
}