2nd Greatest Distance

AtCoder

IDarc121_a

Time2000ms

Memory256MB

Difficulty—

There are $N$ houses numbered $1$ through $N$ on a two-dimensional plane. House $i$ is at $(x_i, y_i)$. We use Chebyshev distance to calculate the distance between two houses. That is, the distance between Houses $i$ and $j$ is $\max(|x_i - x_j|, |y_i-y_j|)$. There are $\frac{N(N-1)}{2}$ pairs formed by two different houses. For each of these pairs, we will calculate the distance between the houses, and then we will sort these distances in **descending order** to get a sequence of length $\frac{N(N-1)}{2}$. Find the second value from the beginning of this sequence. ## Constraints * All values in input are integers. * $3 \leq N \leq 2 \times 10^{5}$ * $-10^{9} \leq x_i, y_i \leq 10^{9}$ ## Input Input is given from Standard Input in the following format: $N$ $x_{1}$ $y_{1}$ $\vdots$ $x_{N}$ $y_{N}$ [samples]

Samples

Input #1

Output #1

3

*   The distance between Houses $1$ and $2$ is $2$;
*   The distance between Houses $1$ and $3$ is $4$;
*   The distance between Houses $2$ and $3$ is $3$.
*   By sorting these in descending order, we get $(4,3,2)$, where the second value from the beginning is $3$.

Input #2

Output #2

1

*   There may be multiple houses at the same coordinates.

Input #3

Output #3

API Response (JSON)

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    "platform": "AtCoder",
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      "memory_limit": 262144
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "arc121_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ houses numbered $1$ through $N$ on a two-dimensional plane. House $i$ is at $(x_i, y_i)$.\nWe use Chebyshev distance to calculate the distance between two houses. That is, the distance be...",
      "is_translate": false,
      "language": "English"
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