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 (1.14.1) (judge verdict: Accepted)

package main

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

func main() {
	var n, c int
	fmt.Scan(&n, &c)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	ds := make([][]int, c)
	for i := range ds {
		ds[i] = make([]int, c)
		for j := range ds[i] {
			sc.Scan()
			ds[i][j], _ = strconv.Atoi(sc.Text())
		}
	}
	cs := make([][]int, n)
	for i := range cs {
		cs[i] = make([]int, n)
		for j := range cs[i] {
			sc.Scan()
			cs[i][j], _ = strconv.Atoi(sc.Text())
			cs[i][j]--
		}
	}
	d1 := make([]int, c)
	d2 := make([]int, c)
	d3 := make([]int, c)
	for cl := 0; cl < c; cl++ {
		var s1, s2, s3 int
		for i := 0; i < n; i++ {
			for j := 0; j < n; j++ {
				switch (i + j) % 3 {
				case 0:
					s1 += ds[cs[i][j]][cl]
				case 1:
					s2 += ds[cs[i][j]][cl]
				case 2:
					s3 += ds[cs[i][j]][cl]
				}
			}
		}
		d1[cl] = s1
		d2[cl] = s2
		d3[cl] = s3
	}

	mi := int(1e10)
	for c1 := 0; c1 < c; c1++ {
		for c2 := 0; c2 < c; c2++ {
			if c2 == c1 {
				continue
			}
			for c3 := 0; c3 < c; c3++ {
				if c3 == c1 || c3 == c2 {
					continue
				}
				mi = min(mi, d1[c1]+d2[c2]+d3[c3])
			}
		}
	}

	fmt.Println(mi)
}

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

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}