Loong and Takahashi

AtCoder

IDabc335_d

Time2000ms

Memory256MB

Difficulty—

There is a grid with $N$ rows and $N$ columns, where $N$ is an odd number at most $45$. Let $(i,j)$ denote the cell at the $i$\-th row from the top and $j$\-th column from the left. In this grid, you will place Takahashi and a dragon consisting of $N^2-1$ parts numbered $1$ to $N^2-1$ in such a way that satisfies the following conditions: * Takahashi must be placed at the center of the grid, that is, in cell $(\frac{N+1}{2},\frac{N+1}{2})$. * Except for the cell where Takahashi is, exactly one dragon part must be placed in each cell. * For every integer $x$ satisfying $2 \leq x \leq N^2-1$, the dragon part $x$ must be placed in a cell adjacent by an edge to the cell containing part $x-1$. * Cells $(i,j)$ and $(k,l)$ are said to be adjacent by an edge if and only if $|i-k|+|j-l|=1$. Print one way to arrange the parts to satisfy the conditions. It is guaranteed that there is at least one arrangement that satisfies the conditions. ## Constraints * $3 \leq N \leq 45$ * $N$ is odd. ## Input The input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

1 2 3 4 5
16 17 18 19 6
15 24 T 20 7
14 23 22 21 8
13 12 11 10 9

The following output also satisfies all the conditions and is correct.

9 10 11 14 15
8 7 12 13 16
5 6 T 18 17
4 3 24 19 20 
1 2 23 22 21

On the other hand, the following outputs are incorrect for the reasons given.
Takahashi is not at the center.

1 2 3 4 5
10 9 8 7 6
11 12 13 14 15
20 19 18 17 16
21 22 23 24 T

The cells containing parts $23$ and $24$ are not adjacent by an edge.

1 2 3 4 5
10 9 8 7 6
11 12 24 22 23
14 13 T 21 20
15 16 17 18 19

API Response (JSON)

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  "problem": {
    "name": "Loong and Takahashi",
    "description": {
      "content": "There is a grid with $N$ rows and $N$ columns, where $N$ is an odd number at most $45$. Let $(i,j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left. In this grid, you ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc335_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $N$ rows and $N$ columns, where $N$ is an odd number at most $45$.\nLet $(i,j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left.\nIn this grid, you ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments