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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    let s: Vec<usize> = read_vec();
    let (N, C) = (s[0], s[1]);
    let mut D = vec![vec![0; C]; C];
    for i in 0..C {
        let s: Vec<i32> = read_vec();
        for j in 0..C {
            D[i][j] = s[j];
        }
    }
    let D = D;
    let mut c = vec![vec![0usize; N]; N];
    for i in 0..N {
        let s: Vec<usize> = read_vec();
        for j in 0..N {
            c[i][j] = s[j] - 1;
        }
    }
    let c = c;
    // println!("{:?}", D);
    // println!("{:?}", c);

    let mut groups = vec![vec![0usize; 0]; 3];
    for i in 0..N {
        for j in 0..N {
            groups[(i + j) % 3].push(c[i][j]);
        }
    }

    let groups = groups;
    let mut group_dict: Vec<std::collections::HashMap<usize, i32>> =
        vec![std::collections::HashMap::new(); 3];
    for i in 0..3 {
        for color in 0..C {
            group_dict[i].insert(color, 0);
        }
        for color in &groups[i] {
            (*group_dict[i].entry(*color).or_insert(0)) += 1;
        }
    }
    // println!("{:?}", group_dict);

    let mut cost_dict: Vec<std::collections::HashMap<usize, i32>> =
        vec![std::collections::HashMap::new(); 3];
    for i in 0..3 {
        for src_color in 0..C {
            for dst_color in 0..C {
                (*cost_dict[i].entry(dst_color).or_insert(0)) +=
                D[src_color][dst_color] * group_dict[i][&src_color];
            }
        }
    }
    // println!("{:?}", cost_dict);

    let mut ans = std::i32::MAX;
    for group_idx in 0..3 {
        for c_idx1 in 0..C {
            let cost1 = cost_dict[0][&c_idx1];
            for c_idx2 in 0..C {
                if c_idx1 == c_idx2 {
                    continue;
                }
                let cost2 = cost_dict[1][&c_idx2];
                for c_idx3 in 0..C {
                    if c_idx1 == c_idx3 || c_idx2 == c_idx3 {
                        continue;
                    }
                    let cost3 = cost_dict[2][&c_idx3];
                    ans = std::cmp::min(ans, cost1 + cost2 + cost3);
                }
            }
        }
    }
    println!("{:?}", ans);
}