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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

var (
	readString func() string
	stdout     *bufio.Writer
)

func init() {
	readString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

func readInt() int {
	i, err := strconv.Atoi(readString())
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = readInt()
	}
	return b
}

func readLengthAndSlice() []int {
	n := readInt()
	return readIntSlice(n)
}

func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(stdout, f, args...)
}

func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(stdout, args...)
}

func vi(n int, args ...int) []int {
	res := make([]int, n)
	if len(args) == 0 {
		return res
	}
	v := args[0]
	if v == 0 {
		return res
	}
	for i := 0; i < n; i++ {
		res[i] = v
	}
	return res
}

func vvi(n int, args ...int) [][]int {
	res := make([][]int, n)
	m := n
	if len(args) > 0 {
		m = args[0]
	}
	v := 0
	if len(args) > 1 {
		v = args[1]
	}
	for i := 0; i < n; i++ {
		res[i] = vi(m, v)
	}
	return res
}

func min(a, b int) int {
	if a < b {
		return a
	} else {
		return b
	}
}

func main() {
	defer stdout.Flush()

	N := readInt()
	C := readInt()
	D := vvi(C + 1)
	for i := 1; i <= C; i++ {
		for j := 1; j <= C; j++ {
			D[i][j] = readInt()
		}
	}

	es := vvi(3, C+1)
	for i := 1; i <= N; i++ {
		for j := 1; j <= N; j++ {
			c := readInt()
			es[(i+j)%3][c]++
		}
	}

	ans := int(2e+10)
	for i := 1; i <= C; i++ {
		for j := 1; j <= C; j++ {
			if i == j {
				continue
			}
			for k := 1; k <= C; k++ {
				if i == k || j == k {
					continue
				}
				score := 0
				for l := 1; l <= C; l++ {
					score += es[0][l]*D[l][i] + es[1][l]*D[l][j] + es[2][l]*D[l][k]
				}
				ans = min(ans, score)
			}
		}
	}
	println(ans)
}