You have a given picture with size $w \times h$. Determine if the given picture has a single "+" shape or not. A "+" shape is described below:

A "+" shape has one center nonempty cell. There should be some (at least one) consecutive non-empty cells in each direction (left, right, up, down) from the center. In other words, there should be a ray in each direction. All other cells are empty.

Find out if the given picture has single "+" shape.

-----Input-----

The first line contains two integers $h$ and $w$ ($1 \le h$, $w \le 500$) — the height and width of the picture.

The $i$-th of the next $h$ lines contains string $s_{i}$ of length $w$ consisting "." and "" where "." denotes the empty space and "" denotes the non-empty space.

-----Output-----

If the given picture satisfies all conditions, print "YES". Otherwise, print "NO".

You can output each letter in any case (upper or lower).

-----Examples-----

Input 5 6 ...... ..... .**. ..... ..*...

Output YES

Input 3 5 .... **. ....

Output NO

Input 7 7 ....... ...... ..**. ...... ...... ....... ......

Output NO

Input 5 6 .... ....

.... ....

Output NO

Input 3 7 ..... . .....

Output NO

Input 5 10 .......... ......... ..**. ..*....... ..........

Output NO

-----Note-----

In the first example, the given picture contains one "+".

In the second example, two vertical branches are located in a different column.

In the third example, there is a dot outside of the shape.

In the fourth example, the width of the two vertical branches is $2$.

In the fifth example, there are two shapes.

In the sixth example, there is an empty space inside of the shape.