Coloring Torus

AtCoder

IDagc030_c

Time2000ms

Memory256MB

Difficulty—

For an $n \times n$ grid, let $(r, c)$ denote the square at the $(r+1)$\-th row from the top and the $(c+1)$\-th column from the left. A _good_ coloring of this grid using $K$ colors is a coloring that satisfies the following: * Each square is painted in one of the $K$ colors. * Each of the $K$ colors is used for some squares. * Let us number the $K$ colors $1, 2, ..., K$. For any colors $i$ and $j$ ($1 \leq i \leq K, 1 \leq j \leq K$), every square in Color $i$ has the same number of adjacent squares in Color $j$. Here, the squares adjacent to square $(r, c)$ are $((r-1)\; mod\; n, c), ((r+1)\; mod\; n, c), (r, (c-1)\; mod\; n)$ and $(r, (c+1)\; mod\; n)$ (if the same square appears multiple times among these four, the square is counted that number of times). Given $K$, choose **$n$ between $1$ and $500$** (inclusive) freely and construct a good coloring of an $n \times n$ grid using $K$ colors. It can be proved that this is always possible under the constraints of this problem, ## Constraints * $1 \leq K \leq 1000$ ## Input Input is given from Standard Input in the following format: $K$ [samples]

Samples

Input #1

Output #1

3
1 1 1
1 1 1
2 2 2

*   Every square in Color $1$ has three adjacent squares in Color $1$ and one adjacent square in Color $2$.
*   Every square in Color $2$ has two adjacent squares in Color $1$ and two adjacent squares in Color $2$.

Output such as the following will be judged incorrect:

2
1 2
2 2

3
1 1 1
1 1 1
1 1 1

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Coloring Torus",
    "description": {
      "content": "For an $n \\times n$ grid, let $(r, c)$ denote the square at the $(r+1)$\\-th row from the top and the $(c+1)$\\-th column from the left. A _good_ coloring of this grid using $K$ colors is a coloring tha",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc030_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For an $n \\times n$ grid, let $(r, c)$ denote the square at the $(r+1)$\\-th row from the top and the $(c+1)$\\-th column from the left. A _good_ coloring of this grid using $K$ colors is a coloring tha...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments