Problem Statement

There is a grid $X$ with $H$ rows and $W$ columns, where each cell is painted white or black. The colors of the cells of grid $X$ are represented by $H$ strings $S_1, \cdots, S_H$ of length $W$ consisting of # and .: if the $j$-th character of $S_i$ is #, the cell $(i, j)$ in the $i$-th row from the top and the $j$-th column from the left is black, and if it is ., the cell is white.

Grid $X$ is said to be generable by a stamp of size $k$ if, for a grid $Y$ with $H$ rows and $W$ columns whose cells are all white, it is possible to choose a positive integer $k$ that is at most $H$ and at most $W$ and make it match grid $X$ by performing the following operation any number of times.

(Operation)
Choose a pair of integers $(i, j)$ satisfying $1 \leq i \leq H-k+1$ and $1 \leq j \leq W-k+1$, and for all integers $(l, m)$ satisfying $i \leq l \leq i+k-1$ and $j \leq m \leq j+k-1$, if the color of cell $(l, m)$ of grid $Y$ is white, repaint that cell black.

Find the maximum size of a stamp that can generate grid $X$.

Input

$H\ W$
$S_1$
$\vdots$
$S_H$

The input satisfies the following constraints.

• $H, W$ are integers
• $1 \leq H \leq 2000$
• $1 \leq W \leq 2000$
• $S_i$ is a string of length $W$ consisting only of # and .
• There exists at least $1$ pair $(i, j)$ such that the $j$-th character of $S_i$ is #.

Output

Print the maximum size of a stamp that can generate grid $X$. Print a newline at the end.

Sample

Sample 1

Input

3 3
##.
###
.##

Output

2

Grid $Y$ is initially in the following state.

Consider the case $k=2$.

First, choose $(1,1)$ and perform the operation. Grid $Y$ then becomes as follows.

Next, choose $(2,2)$ and perform the operation. Grid $Y$ then becomes as follows, which matches grid $X$.

When $k\geq 3$, grid $X$ cannot be generated, so the answer is $2$.

3 3
###
###
###

3

5 6
###.##
##.###
#####.
.###..
######

1