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)

#[allow(unused_imports)] use proconio::{input, marker::{Bytes, Chars, Usize1, Isize1}};
#[allow(unused_imports)] use std::cmp::{min, max};
#[allow(unused_imports)] use superslice::Ext as _;

#[proconio::fastout]
fn main() {
	input! {
		n: usize,
		cnum: usize,
		d: [[usize; cnum]; cnum],
		c: [[Usize1; n]; n],
	}

	let inf = 99999999999999usize;

	// 各マスを、(i+j)%3 = 0 or 1 or 2 の3つのグループに分割する。 
	// 各グループについて、C通りの色を塗りつぶしたときの違和感の和を前処理しておき, 
	// C^3通りの組み合わせを検証して最小値を出力する

	// 前処理
	let mut cost = vec![vec![0usize; cnum]; 3];
	for color in 0..cnum {
		for i in 0..n {
			for j in 0..n {
				cost[(i+j)%3][color] += d[c[i][j]][color];
			}
		}
	}

	// 解を求める
	let mut ans = inf;
	for c0 in 0..cnum {
		for c1 in 0..cnum {
			if c0 == c1 {
				continue;
			}
			for c2 in 0..cnum {
				if c2 == c0 || c2 == c1 {
					continue;
				}
				let mut tmp = 0usize;
				tmp += cost[0][c0];
				tmp += cost[1][c1];
				tmp += cost[2][c2];
				ans = min(ans, tmp);
			}
		}
	}

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