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: Accepted)

n, c = gets.chomp.split.map(&:to_i)

colors_diff = c.times.map do
 gets.chomp.split.map(&:to_i)
end

colors = (1..c).to_a.zip([0]*(1..c).to_a.size).to_h

zone0 = colors.dup
zone1 = colors.dup
zone2 = colors.dup

# zoneごとに、さらにcolorごとに何個有るか見ておく。
n.times do |i|
  row = gets.chomp.split.map(&:to_i)
  row.each_with_index do |attr, j|
    case (i + j + 2) % 3
    when 0
      zone0[attr] += 1
    when 1
      zone1[attr] += 1
    when 2
      zone2[attr] += 1
    end
  end
end

evaluations = []
(1..c).to_a.permutation(3) do |l, m, n|
  evaluation = zone0.reduce(0) do |sum, (k, v)|
    sum + colors_diff[k - 1][l - 1] * v
  end
  evaluation = zone1.reduce(evaluation) do |sum, (k, v)|
    sum + colors_diff[k - 1][m - 1] * v
  end
  evaluation = zone2.reduce(evaluation) do |sum, (k, v)|
    sum + colors_diff[k - 1][n - 1] * v
  end
  evaluations.push evaluation
end
puts evaluations.min