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.

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.

Constraints

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

Sample Input 1

3 4
2221
?1??
2?21

Sample Output 1

Yes

For example, the following placement satisfies the conditions.

Sample Input 2

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

Sample Output 2

No

There is no placement that satisfies the conditions.

Sample Input 3

5 5
11111
11111
11211
11111
11111

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分