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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.Array.IO
import Data.Array.Unboxed
import Data.List
import Control.Monad
import Control.Applicative

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

main = do
  (n:c:_) <- getLine >>= return . map read . words :: IO [Int]
  darr <- newArray ((1,1),(c,c)) 0 :: IO (IOUArray (Int, Int) Int)

  forM_ [1..c] $ \i -> do
    temp <- getLine >>= return . map read . words :: IO [Int]
    forM_ (zip [1..c] temp) $ \(j, d) -> do
      writeArray darr (i,j) d

  countArray <- newArray ((0,1),(2,c)) 0 :: IO (IOUArray (Int,Int) Int)
  
  forM_ [1..n] $ \i -> do
    temp <- getLine >>= return . map read . words :: IO [Int]
    forM_ (zip [1..n] temp) $ \(j, c) -> do
      modifyArray countArray (mod (i+j) 3, c) (+1)

  s <- forM [[i,j,k]| i<-[1..c], j<-[1..c], k<-[1..c], i/=j, j/=k, i/=k] $ \colors -> do
    c <- forM [0..2] $ \m -> do
      forM [1..c] $ \x -> do
        count <- readArray countArray (m,x)
        d <- readArray darr (x,colors!!m)
        return $ d * count
    return $ (sum . map sum) c

  print $ minimum s