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: Runtime Error)

require 'Matrix'

N, C = gets.chomp.split(" ").map(&:to_i)
D = []
C.times{
  D << gets.chomp.split(" ").map(&:to_i)
}
G = Array.new(3)
(0..2).each{|i| G[i] = Array.new(C, 0)}
N.times{|i|
  wk = gets.chomp.split(" ").map(&:to_i)
  (0...wk.size).each{|j| G[(i+j+2) % 3][wk[j]-1] += 1}
}

M = Matrix.rows(D, false)
MG = Matrix.rows(G, false)
t = MG * M
c = []
(0..2).each{|i|
  c << t.row(i).to_a.each_with_index.sort_by{|x, | x}[0, 3]
}
ans = c[0].product(c[1], c[2]).select{|i, j, k| i[1]!=j[1] && j[1]!=k[1] && i[1]!=k[1]}.map{|(x, i), (y, j), (z, k)| [x+y+z, i, j, k]}.sort_by{|x, | x}

puts ans.first[0]