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)

N,C = map(int,input().split())
 
D = []
c = []
 
for i in range(C):
    D.append(list(map(int,input().split())))
for i in range(N):
    c.append(list(map(int,input().split()))) 
 
c1 = []
c2 = []
c3 = []
 
from itertools import product
 
for i,j in product(range(N),repeat=2):
    if (i+j)%3 == 0:
        c1.append(c[i][j])
    elif (i+j)%3 == 1:
        c2.append(c[i][j])
    else:
        c3.append(c[i][j])
val=[]
cnt=[[],[],[]]
 
 
for j in range(C):
    cnt[0].append(c1.count(j+1))
    cnt[1].append(c2.count(j+1))
    cnt[2].append(c3.count(j+1))
 
for i in product(range(C),repeat=3):
    dif = 0
    if i[0]!=i[1] and i[1]!=i[2] and i[2]!=i[0]:
        for j in range(C):
            dif += D[j][i[0]] * cnt[0][j]
            dif += D[j][i[1]] * cnt[1][j]
            dif += D[j][i[2]] * cnt[2][j]
        val.append(dif)
 
print(min(val))