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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use proconio::marker::Usize1;
use std::cmp;
use std::collections::HashMap;

fn main() {
    input! {
        n: usize,
        c: usize,
        costs: [[usize; c]; c],
        grid: [[Usize1; n]; n],
    }

    // group iには何色が何個あるか
    let mut data = vec![HashMap::new(); 3];
    for i in 0..n {
        for j in 0..n {
            let index = ((i + 1) + (j + 1)) % 3;
            let entry = data[index].entry(grid[i][j]).or_insert(0);
            *entry += 1;
        }
    }

    let mut min = std::usize::MAX;
    // group 1 -> color i
    // group 2 -> color j
    // group 3 -> color k
    for i in 0..c {
        for j in 0..c {
            for k in 0..c {
                if i == j || j == k || k == i {
                    continue;
                }
                let mut tmp = 0;
                for (key, value) in &data[0] {
                    tmp += costs[*key][i] * value;
                }
                for (key, value) in &data[1] {
                    tmp += costs[*key][j] * value;
                }
                for (key, value) in &data[2] {
                    tmp += costs[*key][k] * value;
                }
                min = cmp::min(min, tmp);
            }
        }
    }
    println!("{}", min);
}