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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import kotlin.system.measureTimeMillis

val dGrid = mutableListOf<List<Int>>()
var C = 0

val list0M = mutableMapOf<Int,Int>()
val list1M = mutableMapOf<Int,Int>()
val list2M = mutableMapOf<Int,Int>()
fun main(args: Array<String>) {
    val (n, c) = readLine()!!.split(" ").map(String::toInt)
    C = c
    val list0 = mutableListOf<Int>()
    val list1 = mutableListOf<Int>()
    val list2 = mutableListOf<Int>()

    for (i in 1..c) {
        dGrid.add(readLine()!!.split(' ').map(String::toInt))
    }

    for (i in 1..n) {
        val cList = readLine()!!.split(' ').map(String::toInt)
        list0.addAll(cList.filterIndexed { index, it -> (index + i + 1) % 3 == 0 })
        list1.addAll(cList.filterIndexed { index, it -> (index + i + 1) % 3 == 1 })
        list2.addAll(cList.filterIndexed { index, it -> (index + i + 1) % 3 == 2 })
    }

    for (i in 1..c) {
        list0M[i] = list0.filter { it == i }?.size?:0
        list1M[i] = list1.filter { it == i }?.size?:0
        list2M[i] = list2.filter { it == i }?.size?:0
    }
    val millis = measureTimeMillis { run() }
    println(millis)

}

private fun run() {



    var min = Long.MAX_VALUE
    for (c1 in 1..C) {
        for (c2 in 1..C) {
            if (c1 == c2) continue
            for (c3 in 1..C) {
                if ((c1 == c2) || (c2 == c3) || (c1 == c3)) continue

                val sum = calcD(c1, list0M) + calcD(c2, list1M) + calcD(c3, list2M)
                min = Math.min(sum, min)
            }
        }
    }
    println(min)
}

fun calcD(c: Int, map: Map<Int, Int>): Long {
    var sum = 0L
    for (i in 1..C) {
        sum += dGrid[i - 1][c - 1] * map!![i]!!
    }
    return sum
}