Plus from Picture

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.

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.

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

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.