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G - Tatami

Score : $600$ points

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.

3 4
2221
?1??
2?21

Yes

For example, the following placement satisfies the conditions.

3 4
2?21
??1?
2?21

No

There is no placement that satisfies the conditions.

5 5
11111
11111
11211
11111
11111

No