Tatami

AtCoder

IDabc285_g

Time3000ms

Memory256MB

Difficulty—

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: $H$ $W$ $c_{1,1}c_{1,2}\ldots c_{1,W}$ $\vdots$ $c_{H,1}c_{H,2}\ldots c_{H,W}$ [samples]

Samples

Input #1

3 4
2221
?1??
2?21

Output #1

Yes

For example, the following placement satisfies the conditions.
![image](https://img.atcoder.jp/abc285/d984ec33355bac05ecebc41076d9a8df.png)

Input #2

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

Output #2

No

There is no placement that satisfies the conditions.

Input #3

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Tatami",
    "description": {
      "content": "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 wi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc285_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\nWe want to cover this grid wi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments