Problem Statement

Consider a grid with $H$ rows and $W$ columns of squares. Let $(r, c)$ denote the square at the $r$-th row from the top and the $c$-th column from the left. Each square is painted black or white.

The grid is said to be good if and only if the following condition is satisfied:

• From $(1, 1)$, we can reach $(H, W)$ by moving one square right or down repeatedly, while always being on a white square.

Note that $(1, 1)$ and $(H, W)$ must be white if the grid is good.

Your task is to make the grid good by repeating the operation below. Find the minimum number of operations needed to complete the task. It can be proved that you can always complete the task in a finite number of operations.

• Choose four integers $r_0, c_0, r_1, c_1(1 \leq r_0 \leq r_1 \leq H, 1 \leq c_0 \leq c_1 \leq W)$. For each pair $r, c$ ($r_0 \leq r \leq r_1, c_0 \leq c \leq c_1$), invert the color of $(r, c)$ - that is, from white to black and vice versa.

Constraints

• $2 \leq H, W \leq 100$

Sample Input 1Copy

3 3
.##
.#.
##.

Sample Output 1Copy

1

Do the operation with $(r_0, c_0, r_1, c_1) = (2, 2, 2, 2)$ to change just the color of $(2, 2)$, and we are done.

Sample Input 2Copy

2 2
#.
.#

Sample Output 2Copy

2

Sample Input 3Copy

4 4
..##
#...
###.
###.

Sample Output 3Copy

0

No operation may be needed.

Sample Input 4Copy

5 5
.#.#.
#.#.#
.#.#.
#.#.#
.#.#.

Sample Output 4Copy

4