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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
import math
from collections import defaultdict

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N):
    read_all = [tuple(map(int, input().split())) for _ in range(N)]
    return map(list,zip(*read_all))

#################

N,C = II()
D = []
for i in range(C):
    D.append(III())
c = []
for i in range(N):
    c.append(III())

d1 = []
d2 = []
d3 = []
for i in range(N):
    for j in range(N):
        if (i+j)%3==0:
            d1.append(c[i][j])
        elif (i+j)%3==1:
            d2.append(c[i][j])
        else:
            d3.append(c[i][j])

d1val = []
d2val = []
d3val = []

for cl in range(C):
    temp1 = 0
    temp2 = 0
    temp3 = 0
    for dcl in d1:
        temp1 += D[dcl-1][cl]
    for dcl in d2:
        temp2 += D[dcl-1][cl]
    for dcl in d3:
        temp3 += D[dcl-1][cl]
    d1val.append(temp1)
    d2val.append(temp2)
    d3val.append(temp3)

ans = float('inf')
for i in range(C):
    for j in range(C):
        for k in range(C):
            if i==j or i==k or j==k:
                continue
            else:
                temp = d1val[i]+d2val[j]+d3val[k]
                if temp<ans:
                    ans = temp

print(ans)