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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($n,$c) = explode(" ", trim(fgets(STDIN)));

  $d = [];
  for ($i=0; $i<$c; $i++) {
    $d[] = explode(" ", trim(fgets(STDIN)));
  }

  // 余りごとの色の数
  $now_count = [0, 1, 2];
  for($i=0;$i<3;$i++){
    $now_count[$i] = array_fill(1, $c, 0);
  }
  for ($i=0; $i<$n; $i++) {
    $e = explode(" ", trim(fgets(STDIN)));
    for ($j=0; $j<$n; $j++){
      $now_count[(($i+1)+($j+1))%3][$e[$j]]++;
    }
  }

  $ans = PHP_INT_MAX;
  for ($i=0; $i<$c; $i++) {
    $isum = 0;
    foreach($now_count[0] as $key => $value){
      $isum += $d[$key-1][$i] * $value;
    }
    for ($j=0; $j<$c; $j++) {
      if($i==$j){
        continue;
      }
      $jsum = $isum;
      foreach($now_count[1] as $key => $value){
        $jsum += $d[$key-1][$j] * $value;
      }

      for ($k=0; $k<$c; $k++) {
        if($i==$k || $j==$k){
          continue;
        }
        $ksum = $jsum;
        foreach($now_count[2] as $key => $value){
          $ksum += $d[$key-1][$k] * $value;
        }
        $ans = min($ans, $ksum);
      }
    }
  }

  echo $ans;