Score : $1000$ points

Problem Statement

Note the unusual memory limit.

For a rectangular grid where each square is painted white or black, we define its complexity as follows:

• If all the squares are black or all the squares are white, the complexity is $0$.
• Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let $c_1$ and $c_2$ be the complexities of the subgrids. There can be multiple ways to perform the division, and let $m$ be the minimum value of $\max(c_1, c_2)$ in those divisions. The complexity of the grid is $m+1$.

You are given a grid with $H$ horizontal rows and $W$ vertical columns where each square is painted white or black. $HW$ characters from $A_{11}$ to $A_{HW}$ represent the colors of the squares. $A_{ij}$ is # if the square at the $i$-th row from the top and the $j$-th column from the left is black, and $A_{ij}$ is . if that square is white.

Find the complexity of the given grid.

Constraints

• $1 \leq H,W \leq 185$
• $A_{ij}$ is # or ..

Input

Input is given from Standard Input in the following format:

$H$ $W$

$A_{11}$$A_{12}$$...$$A_{1W}$

$:$

$A_{H1}$$A_{H2}$$...$$A_{HW}$

Output

Print the complexity of the given grid.

3 3
...
.##
.##

2

Let us divide the grid by the boundary line between the first and second columns. The subgrid consisting of the first column has the complexity of $0$, and the subgrid consisting of the second and third columns has the complexity of $1$, so the whole grid has the complexity of at most $2$.

6 7
.####.#
#....#.
#....#.
#....#.
.####.#
#....##

4