Practice Flood fill and Backtracking with the exercise "Optimized coloring"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

Having an empty sheet of paper divided into some zones, try to fill these zones with as few colors as possible, respecting the following rule : two adjacent zones must be filled with two different colors.

A zone is made of "space" characters.

For exemple :


/\
\/

is not a zone, while


+-+
|1|
\-/

is one (1 space, denoted with the "1" symbol).

Each ASCII character fills a "cell" of the sheet of paper : the shape of the characters have no importance, it's just aestethic.

Two zones are considered as adjacent if they share, at least partially, a border.

For instance, these pairs of zones are adjacent :

+---+         +---+
|   +---+     |   |
+---|   |     +-+-+-+
    +---+       |   |
                +---+

Warning : two zones touching diagonally are not adjacent.

For instance, these zones are not adjacent :

+---+
|   |
+---+---+
    |   |
    +---+

You have to find the minimum number of colors necessary to fill all the zones.

Input

Line 1: an integer w representing the width of the sheet of paper
Line 2: an integer h representing the height of the sheet of paper
h following lines : a string representing one line of the sheet of paper

Output

Line 1: an integer representing the minimum number of colors necessary to fill the sheet of paper

Constraints

w < 100
h < 20

You can find the following symbols in the input : -, |, +, /, \ and _

Example

Input

11
6
+---------+
|         |
|         |
|         |
|         |
+---------+

Output

Solve it

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