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::BufRead;

fn main() {
    let stdin = std::io::stdin();
    let (n, c): (usize, usize) = stdin.lock().gets().split(' ').values();
    let mut diff = Vec::new();
    for line in stdin.lock().lines().take(c).map(|x| x.unwrap()) {
        let x = line.split(' ').map(|x| x.parse().unwrap())
            .collect::<Vec<u32>>();
        diff.push(x);
    }
    let mut color = Vec::new();
    for line in stdin.lock().lines().take(n).map(|x| x.unwrap()) {
        let x = line.split(' ').map(|x| x.parse().unwrap())
            .collect::<Vec<usize>>();
        color.push(x);
    }

    // Total iwakan when line `(x + y) % 3` is repainted in color `new_c`.
    let mut iwasum = vec![vec![0; c]; 3];
    for y in 0..n {
        for x in 0..n {
            for new_c in 0..c {
                let old_c = color[y][x] - 1;
                iwasum[(x + y) % 3][new_c] += diff[old_c][new_c];
            }
        }
    }
    let mut ans = std::u32::MAX;
    for c0 in 0..c {
        for c1 in (0..c).filter(|&x| x != c0) {
            for c2 in (0..c).filter(|&x| x != c0 && x != c1) {
                ans = std::cmp::min(
                    ans, iwasum[0][c0] + iwasum[1][c1] + iwasum[2][c2]);
            }
        }
    }
    println!("{}", ans);
}

trait Gets { fn gets(&mut self) -> String; }
impl<T: std::io::BufRead> Gets for T {
    fn gets(&mut self) -> String { self.lines().next().unwrap().unwrap() } }

trait Values<T> { fn values(&mut self) -> T; }
impl<'a, I, T1, T2> Values<(T1, T2)> for I
    where I: Iterator<Item=&'a str>,
          T1: std::str::FromStr, T1::Err: std::fmt::Debug,
          T2: std::str::FromStr, T2::Err: std::fmt::Debug {
    fn values(&mut self) -> (T1, T2) {
        (self.next().unwrap().parse().unwrap(),
         self.next().unwrap().parse().unwrap())
    }
}