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"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
	sc.Split(bufio.ScanWords)
	sc.Scan()
	n, _ := strconv.Atoi(sc.Text())
	sc.Scan()
	c, _ := strconv.Atoi(sc.Text())

	d := make([][]int, c)
	for i := 0; i < c; i++ {
		d[i] = make([]int, c)
		for j := 0; j < c; j++ {
			sc.Scan()
			d[i][j], _ = strconv.Atoi(sc.Text())
		}
	}

	a := make([][]int, n)
	for i := 0; i < n; i++ {
		a[i] = make([]int, n)
		for j := 0; j < n; j++ {
			sc.Scan()
			a[i][j], _ = strconv.Atoi(sc.Text())
			a[i][j]--
		}
	}

	change := make([][]int, 3)
	for i := 0; i < 3; i++ {
		change[i] = make([]int, c)
	}
	//fmt.Println(change)
	for s := 0; s < 3; s++ {
		for color := 0; color < c; color++ {
			for i := 0; i < n; i++ {
				for j := 0; j < n; j++ {
					if (i+j)%3 != s {
						continue
					}
					change[s][color] += d[a[i][j]][color]
				}
			}
		}
	}
	//fmt.Println(change)

	ans := int(1e9)
	for c0 := 0; c0 < c; c0++ {
		for c1 := 0; c1 < c; c1++ {
			if c0 == c1 {
				continue
			}
			for c2 := 0; c2 < c; c2++ {
				if c0 == c2 || c1 == c2 {
					continue
				}
				res := change[0][c0] + change[1][c1] + change[2][c2]
				if ans > res {
					ans = res
				}
			}
		}
	}
	fmt.Println(ans)
}