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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function equal(a, b) {
    var aP = Object.getOwnPropertyNames(a);
    var bP = Object.getOwnPropertyNames(b);
    if (aP.length != bP.length)
        return false;
    for (var i = 0; i < aP.length; i++)
        if (a[aP[i]] !== b[aP[i]])
            return false;
    return true;
}
function pi(text) {
    return parseInt(text, 10);
}
var six = [6, 5, 4, 3, 2, 1].map(_ => Math.pow(6, _));
var nine = [5, 4, 3, 2, 1].map(_ => Math.pow(9, _));
function count(i) {
    if (i < 6)
        return i;
    if (i < 9)
        return 1 + (i - 6);
    return Math.min(count(i - six.find(_ => _ <= i)) + 1, count(i - nine.find(_ => _ <= i)) + 1);
}
function main(input) {
    var l = input.split("\n");
    var T = l.shift().split(" ").map(_ => pi(_));
    var N = T[0];
    var C = T[1];
    var D = l.splice(0, C).map(_ => _.split(" ").map(_ => pi(_)));
    var c = l.splice(0, N).map(_ => _.split(" ").map(_ => pi(_)));
    var mod2colorStat = [".".repeat(C).split("").map(_ => 0), ".".repeat(C).split("").map(_ => 0), ".".repeat(C).split("").map(_ => 0)];
    c.forEach((_, i) => _.forEach((_, j) => {
        mod2colorStat[(i + j) % 3][_ - 1]++;
    }));
    var mod2score = mod2colorStat.map(stat => {
        return ".".repeat(C).split("").map((_, toColor) => stat.map((count, fromColor) => fromColor == toColor ? 0 : count * D[fromColor][toColor]).reduce((a, b) => a + b, 0));
    });
    var minScore = Infinity;
    for (let a = 0; a < C; a++) {
        for (let b = 0; b < C; b++) {
            if (a == b)
                continue;
            for (let c = 0; c < C; c++) {
                if (b == c || a == c)
                    continue;
                minScore = Math.min(minScore, mod2score[0][a] + mod2score[1][b] + mod2score[2][c]);
            }
        }
    }
    console.log(minScore);
}
main(require("fs").readFileSync("/dev/stdin", "utf8"));