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 Python (3.4.3) (judge verdict: Accepted)

import itertools
import os
import sys

import numpy as np

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353


# 色のパターン 30*29*28 == 24360
# 全部試すだけ

N, C = list(map(int, sys.stdin.buffer.readline().split()))
D = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(C)]
S = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(N)]

D = np.array(D, dtype=int)
S = np.array(S, dtype=int) - 1

md = np.zeros((N, N), dtype=int)
md += np.arange(N, dtype=int)
md += np.arange(N, dtype=int)[:, None]
md %= 3

# s += D[S[md == 0], colors[0]].sum()
# s += D[S[md == 1], colors[1]].sum()
# s += D[S[md == 2], colors[2]].sum()

# costs[d][c]: md == d の場所を c に変えるときのコスト
costs = [[0] * C for _ in range(3)]
for d in range(3):
    for c in range(C):
        # md == d の場所を c に変えるときのコスト
        costs[d][c] = D[S[md == d], c].sum()

ans = INF
for colors in itertools.permutations(range(C), r=3):
    ans = min(ans, costs[0][colors[0]] + costs[1][colors[1]] + costs[2][colors[2]])
print(ans)