Domino Quality

AtCoder

IDagc041_c

Time2000ms

Memory256MB

Difficulty—

Let us consider a grid of squares with $N$ rows and $N$ columns. You want to put some domino pieces on this grid. Each domino piece covers two squares that have a common side. Each square can be covered by at most one piece. For each row of the grid, let's define its quality as the number of domino pieces that cover at least one square in this row. We define the quality of each column similarly. Find a way to put at least one domino piece on the grid so that the quality of every row is equal to the quality of every column, or determine that such a placement doesn't exist. ## Constraints * $2 \le N \le 1000$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

aabb..
b..zz.
ba....
.a..aa
..a..b
..a..b

The quality of every row and every column is 2.

Input #2

Output #2

\-1

API Response (JSON)

{
  "problem": {
    "name": "Domino Quality",
    "description": {
      "content": "Let us consider a grid of squares with $N$ rows and $N$ columns. You want to put some domino pieces on this grid. Each domino piece covers two squares that have a common side. Each square can be cover",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc041_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let us consider a grid of squares with $N$ rows and $N$ columns. You want to put some domino pieces on this grid. Each domino piece covers two squares that have a common side. Each square can be cover...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments