Flags

AtCoder

IDarc069_d

Time5000ms

Memory256MB

Difficulty—

Snuke loves flags. Snuke is placing $N$ flags on a line. The $i$\-th flag can be placed at either coordinate $x_i$ or coordinate $y_i$. Snuke thinks that the flags look nicer when the smallest distance between two of them, $d$, is larger. Find the maximum possible value of $d$. ## Constraints * $2 ≤ N ≤ 10^{4}$ * $1 ≤ x_i, y_i ≤ 10^{9}$ * $x_i$ and $y_i$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $:$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

4

The optimal solution is to place the first flag at coordinate $1$, the second flag at coordinate $5$ and the third flag at coordinate $9$. The smallest distance between two of the flags is $4$ in this case.

Input #2

Output #2

0

There can be more than one flag at the same position.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Flags",
    "description": {
      "content": "Snuke loves flags. Snuke is placing $N$ flags on a line. The $i$\\-th flag can be placed at either coordinate $x_i$ or coordinate $y_i$. Snuke thinks that the flags look nicer when the smallest distanc",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc069_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke loves flags.\nSnuke is placing $N$ flags on a line.\nThe $i$\\-th flag can be placed at either coordinate $x_i$ or coordinate $y_i$.\nSnuke thinks that the flags look nicer when the smallest distanc...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments