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;
use std::str::FromStr;
use std::collections::HashMap;
use std::cmp::min;

type Pair = (u64, u64);

fn input_tuple() -> (usize, usize) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<usize> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input_vec() -> Vec<u64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}

fn calc(c: u64, map: &HashMap<u64, u64>, diff: &Vec<Vec<u64>>) -> u64 {
    let mut sum = 0;
    for (k, v) in map {
        if *k - 1 == c {
            continue;
        }
        sum += diff[*k as usize - 1][c as usize] * v;
    }
    sum
}

fn main() {
    let (n, c) = input_tuple();
    let mut diff: Vec<Vec<u64>> = Vec::new();
    let mut colors: Vec<Vec<u64>> = Vec::new();
    let mut elements: Vec<HashMap<u64, u64>> = vec![HashMap::new(); 3];

    for _ in 0..c {
        let d = input_vec();
        diff.push(d);
    }
    for _ in 0..n {
        let c = input_vec();
        colors.push(c);
    }
    for i in 0..n {
        for j in 0..n {
            let n = elements[(i+j) as usize % 3].entry(colors[i][j]).or_insert(0);
            *n += 1;
        }
    }
    let mut ans = std::u64::MAX;
    for i in 0..c {
        for j in 0..c {
            for k in 0..c {
                if i == j || j == k || k == i {
                    continue;
                }
                let tmp = calc(i as u64, &elements[0], &diff)
                    + calc(j as u64, &elements[1], &diff)
                    + calc(k as u64, &elements[2], &diff);
                ans = min(ans, tmp);
                // println!("({}, {}, {}) -> {}", i, j, k, tmp);
            }
        }
    }
    // println!("{:?}", elements);
    println!("{}", ans);
}