Problem Statement

The time limit for this problem is 3s, and it may be difficult to solve in languages other than C++. Using scanf/printf for input and output is recommended.

There are $N^2$ lamps arranged in a grid with $N$ rows and $N$ columns.
The lamp in the $i$-th row from the top and the $j$-th column from the left is called lamp $(i,j)$.
You are given $M$ boards representing the states of the $N^2$ lamps. If $A_{i,j,k}$ is #, lamp $(j,k)$ on the $i$-th board is on, and if it is ., the lamp is off.
For every pair $i,j$ satisfying $1 \le i \lt j \le M$, determine whether the board $A_j$ can be made starting from the board $A_i$ by following the procedure below.

You may perform the following any number of times, possibly zero: choose an integer $k$, then choose and perform one of the operations below.

• For every lamp $(i,j)$ such that $i=k$, turn it off if it is on, and turn it on otherwise.
• For every lamp $(i,j)$ such that $j=k$, turn it off if it is on, and turn it on otherwise.
• For every lamp $(i,j)$ such that $i+j=k$, turn it off if it is on, and turn it on otherwise.
• For every lamp $(i,j)$ such that $i-j=k$, turn it off if it is on, and turn it on otherwise.

Input

$N\ M$
$A_{1,1,1}A_{1,1,2}A_{1,1,3}\dots A_{1,1,N}$
$A_{1,2,1}A_{1,2,2}A_{1,2,3}\dots A_{1,2,N}$
$A_{1,3,1}A_{1,3,2}A_{1,3,3}\dots A_{1,3,N}$
$\hspace{55pt} \vdots$
$A_{1,N,1}A_{1,N,2}A_{1,N,3}\dots A_{1,N,N}$

$A_{2,1,1}A_{2,1,2}A_{2,1,3}\dots A_{2,1,N}$
$A_{2,2,1}A_{2,2,2}A_{2,2,3}\dots A_{2,2,N}$
$A_{2,3,1}A_{2,3,2}A_{2,3,3}\dots A_{2,3,N}$
$\hspace{55pt} \vdots$
$A_{2,N,1}A_{2,N,2}A_{2,N,3}\dots A_{2,N,N}$

$\hspace{60pt} \vdots$

$A_{M,1,1}A_{M,1,2}A_{M,1,3}\dots A_{M,1,N}$
$A_{M,2,1}A_{M,2,2}A_{M,2,3}\dots A_{M,2,N}$
$A_{M,3,1}A_{M,3,2}A_{M,3,3}\dots A_{M,3,N}$
$\hspace{55pt} \vdots$
$A_{M,N,1}A_{M,N,2}A_{M,N,3}\dots A_{M,N,N}$

$1 \le N \le 200$
$2 \le M \le 200$
$N,M$ are integers.
$A_{i,j,k}$ is # or ..

Output

Output in the following format.

$B_{1,2}B_{1,3}B_{1,4}B_{1,5}\dots B_{1,M}$
$B_{2,3}B_{2,4}B_{2,5}\dots B_{2,M}$
$B_{3,4}B_{3,5}\dots B_{3,M}$
$\hspace{17pt} \vdots$
$B_{M - 1,M}$

Sample

5 3
.....
.....
.....
.....
.....

....#
...#.
..#..
.#...
#....

#.##.
#..##
.#.#.
...#.
.#...

10
0

4 6
.#..
.#.#
#.##
.#.#

.###
##..
###.
##..

.#..
#...
.#..
###.

#..#
.##.
####
.#.#

#.##
..#.
###.
....

##.#
##..
#.##
.#..

10101
0101
010
01
0

1 2
.

#

1