Problem Statement

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.

Constraints

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

Input

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}

Output

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