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)

#!/usr/bin/env ruby

# Generated by AtcoderGreedy on 2018-06-10
# ABC099 D

# my lib

module Enumerable
  # work just like String#split,
  # except this method does not use regex match
  # but check whether yield succeeds or not.
  def split
    current = nil
    ret = []
    each do |elem|
      if yield elem
        if current
          ret << current
          current = nil
        end
      elsif current
        current << elem
      else
        current = [elem]
      end
    end
    ret << current if current
    ret
  end
end

class Array
  # truncate tail, opposite of drop
  def clip(amount = 1)
    if amount < 0
      raise ArgumentError, "amount == #{amount}, cannot be negative!"
    end
    take_amount = size - amount
    take_amount < 0 ? [] : take(take_amount)
  end
end

def n_choose_k(n, k)
  return 0 unless (0..n).cover? k
  result = 1
  1.upto(k) do |d|
    result *= n
    result /= d
    n -= 1
  end
  result
end

# end of lib

# Your code here

def read_matrix(c)
  ret = []
  c.times do
    ret << gets.chomp.split(' ').map(&:to_i)
  end
  ret
end

N, C = gets.chomp.split(' ').map(&:to_i)
D = read_matrix(C)
c = read_matrix(N)

# $stderr.puts "(N, C) = (#{N}, #{C})"
# $stderr.puts D.inspect
# $stderr.puts c.inspect

groups = Array.new(3) do |_|
  (1..C).map do |color|
    [color, 0]
  end.to_h
end

# $stderr.puts groups.inspect

N.times do |i|
  N.times do |j|
    color = c[i][j]
    groups[(i+j)%3][color] += 1
  end
end

colors_cands = (1..C).to_a.permutation(3)

diffs = colors_cands.map do |colors|
  total = 0
  (0...3).each do |i|
    to_color = colors[i]
    (1..C).each do |from_color|
      # $stderr.puts "from: #{from_color}, to: #{to_color}"
      total +=
        groups[i][from_color] * D[from_color - 1][to_color - 1]
    end
  end
  total
end

puts diffs.min