You are given a grid of $N$ rows and $M$ columns. The square at the $i$-th row and $j$-th column will be denoted as $(i,j)$. Some of the squares contain an object. All the remaining squares are empty. The state of the grid is represented by strings $S_1,S_2,\cdots,S_N$. The square $(i,j)$ contains an object if $S_{i,j}=$ # and is empty if $S_{i,j}=$ ..
Consider placing $1 \times 2$ tiles on the grid. Tiles can be placed vertically or horizontally to cover two adjacent empty squares. Tiles must not stick out of the grid, and no two different tiles may intersect. Tiles cannot occupy the square with an object.
Calculate the maximum number of tiles that can be placed and any configulation that acheives the maximum.

Input is given from Standard Input in the following format:
$N\ M$
$S_1$
$S_2$
$\vdots$
$S_N$

On the first line, print the maximum number of tiles that can be placed.
On the next $N$ lines, print a configulation that achieves the maximum. Precisely, output the strings $t_1,t_2,\cdots,t_N$ constructed by the following way.

• $t_i$ is initialized to $S_i$.
• For each $(i,j)$, if there is a tile that occupies $(i,j)$ and $(i+1,j)$, change $t_{i,j}$:=v, $t_{i+1,j}$:=^.
• For each $(i,j)$, if there is a tile that occupies $(i,j)$ and $(i,j+1)$, change $t_{i,j}$:=>, $t_{i,j+1}$:=<.

See samples for further information.
You may print any configulation that maximizes the number of tiles.

$1≤N≤100$
$1 \leq M \leq 100$
$S_i$ is a string with length $M$ consists of # and ..