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(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Read, StdoutLock, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_imports)]
use std::str::FromStr;

// good-grid.rs --- Good Grid
// author: Seong Yong-ju <sei40kr@gmail.com>

#[allow(unused_macros)]
macro_rules! get {
  ($t:ty) => {
    {
      let mut line: String = String::new();
      stdin().read_line(&mut line).unwrap();
      line.trim().parse::<$t>().unwrap()
    }
  };
  ($($t:ty),*) => {
    {
      let mut line: String = String::new();
      stdin().read_line(&mut line).unwrap();
      let mut iter = line.split_whitespace();
      (
        $(iter.next().unwrap().parse::<$t>().unwrap(),)*
      )
    }
  };
  ($t:ty; $n:expr) => {
    (0..$n).map(|_|
                get!($t)
    ).collect::<Vec<_>>()
  };
  ($($t:ty),*; $n:expr) => {
    (0..$n).map(|_|
                get!($($t),*)
    ).collect::<Vec<_>>()
  };
  ($t:ty ;;) => {
    {
      let mut line: String = String::new();
      stdin().read_line(&mut line).unwrap();
      line.split_whitespace()
        .map(|t| t.parse::<$t>().unwrap())
        .collect::<Vec<_>>()
    }
  };
  ($t:ty ;; $n:expr) => {
    (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
  };
}

#[allow(unused_macros)]
macro_rules! debug {
  ($($a:expr),*) => {
    println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
  }
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("Failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("Failed to parse token")
}

#[allow(dead_code)]
fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>) -> ()>(f: F) {
    let out = stdout();
    let writer = BufWriter::new(out.lock());
    f(writer);
}

fn main() {
    let (n, m) = get!(usize, usize);
    let d_map = (0..m)
        .map(|_i| (0..m).map(|_j| read::<u32>()).collect::<Vec<_>>())
        .collect::<Vec<_>>();
    let c_map = (0..n)
        .map(|_i| (0..n).map(|_j| read::<u32>() - 1).collect::<Vec<_>>())
        .collect::<Vec<_>>();

    let mut d_sum = vec![vec![0u32; m]; 3];
    for i in 0..n {
        for j in 0..n {
            let x = c_map[i][j];
            for y in 0..m {
                d_sum[(i + j) % 3][y as usize] += d_map[x as usize][y as usize];
            }
        }
    }

    let mut ans = <u32>::max_value();
    for c0 in 0..m {
        for c1 in 0..m {
            for c2 in 0..m {
                if c0 == c1 || c1 == c2 || c2 == c0 {
                    continue;
                }

                ans = min(ans, d_sum[0][c0] + d_sum[1][c1] + d_sum[2][c2]);
            }
        }
    }

    with_bufwriter(|mut out| writeln!(out, "{}", ans).unwrap());
}