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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N, C = gets.split.map(&:to_i)
if N == 1
  puts 0
else
  d = Array.new
  C.times do
    d += [gets.split.map(&:to_i)]
  end
  c = Array.new(3){Array.new(C){0}}
  N.times do |i|
    nums_c = gets.split.map(&:to_i)
    N.times do |j|
      c[(i + j) % 3][nums_c[j] - 1] += 1
    end
  end

  sum_d = Array.new(3){Array.new}
  3.times do |i|
    next if !c[i]
    C.times do |color2|
      sum_d[i][color2] = 0
      c[i].each_with_index{|num, color| sum_d[i][color2] += num * d[color][color2]}
    end
  end

  sum_d.compact!
  size = sum_d.size
  arr = Array.new(size){Array.new}
  size.times do |i|
    max = sum_d[i].max + 1
    size.times do
      min = sum_d[i].min
      min_id = sum_d[i].index(min)
      sum_d[i][min_id] = max
      arr[i] += [[min_id, min]]
    end
  end

  ans = 1000000
  3.times do |i|
    id1, val1 = arr[0][i]
    3.times do |j|
      id2, val2 = arr[1][j]
      next if id2 == id1
      3.times do |k|
        id3, val3 = arr[2][k]
        next if [id1, id2].include?(id3)
        ans = [ans, val1 + val2 + val3].min
      end
    end
  end

  puts ans
end