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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
	integer N, C, i, j, k
	integer(8) ans
	integer, allocatable :: D(:, :), cl(:, :), S(:, :)
	read(*, *) N, C
	allocate(D(1: C, 1:C))
	do i = 1, C
		read(*, *) D(i, 1: C)
	end do
	allocate(cl(1: N, 1:N))
	do i = 1, N
		read(*, *) cl(i, 1:N)
	end do
	allocate(S(1:C, 0:2))
	S(1:C, 0:2) = 0
	do l = 0, 2
		do k = 1, C
			do j = 1, N
				do i = 1, N
					if(mod(i+j, 3) == l) then
						S(k, l) = S(k, l) + D(cl(i,j), k)
					end if
				end do
			end do
		end do
	end do
	ans = 300000000
	do i = 1, C
		do j = 1, C
			do k = 1, C
				if(i /= j .and. j /= k .and. k /= i) then
					ans = min(S(i,0) + S(j,1) + S(k, 2), ans)
				end if
			end do
		end do
	end do
	write(*, *) ans
end program main