We have a grid with $H$ horizontal rows and $W$ vertical columns. We denote by square $(i,j)$ the square at the $i$-th row from the top and $j$-th column from the left.

We want to cover this grid with $1 \times 1$ tiles and $1 \times 2$ tiles so that no tiles overlap and everywhere is covered by a tile. (A tile can be rotated.)

Each square has `1`, `2`, or `?` written on it. The character written on square $(i, j)$ is $c_{i,j}$.  
A square with `1` written on it must be covered by a $1 \times 1$ tile, and a square with `2` by a $1 \times 2$ tile. A square with `?` may be covered by any kind of tile.

Determine if there is such a placement of tiles.

The input is given from Standard Input in the following format:

```
$H$ $W$
$c_{1,1}c_{1,2}\ldots c_{1,W}$
$\vdots$
$c_{H,1}c_{H,2}\ldots c_{H,W}$
```

Print `Yes` if there is a placement of tiles to satisfy the conditions in the Problem Statement; print `No` otherwise.

-   $1 \leq H,W \leq 300$
-   $H$ and $W$ are integers.
-   $c_{i,j}$ is one of `1`, `2`, and `?`.

Yes

For example, the following placement satisfies the conditions.

No

There is no placement that satisfies the conditions.