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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn enumerate_3colors(c: usize) -> Vec<Vec<usize>>{
    let mut v: Vec<Vec<usize>> = vec![];
    for i in 0..c{
        for j in 0..c{
            for k in 0..c{
                v.push(vec![i, j, k]);
            }
        }
    }

    v.into_iter().filter(|x| x[0] != x[1] && x[1] != x[2] && x[2] != x[0]).collect()
}
fn main(){
    let line = read_as_vec::<usize>();
    let (n, c) = (line[0], line[1]);

    let mut diff: Vec<Vec<u64>> = Vec::new();

    for _ in 0..c{
        diff.push(read_as_vec::<u64>());
    }

    let mut grid: Vec<Vec<usize>> = Vec::new();

    for _ in 0..n{
        let line = read_as_vec::<usize>();
        grid.push(line.into_iter().map(|x| x-1).collect());
    }

    let mut grid_counter = vec![vec![0;c];3];

    for i in 0..n{
        for j in 0..n{
            grid_counter[(i+j)%3][grid[i][j]] += 1;
        }
    }

    let grid_counter = grid_counter;
    let enums = enumerate_3colors(c);

    let mut min_cost = std::u64::MAX;
    for color in enums{
        let mut cost = 0;
        for i in 0..3{
            for j in 0..c{
                cost += diff[j][color[i]] * grid_counter[i][j];
            }
        }

        min_cost = cmp::min(min_cost, cost);
    }

    println!("{}", min_cost);
}