Silver Woods

AtCoder

IDabc181_f

Time2000ms

Memory256MB

Difficulty—

On the $xy$\-plane, we have a passage surrounded by the two lines $y=-100$ and $y=100$. In the part of this passage with $-100 < x < 100$, there are $N$ negligibly small nails. The coordinates of the $i$\-th nail are $(x_i, y_i)$. Takahashi will choose a real number $r \ (0 < r \leq 100)$ and put a circle of radius $r$ so that its center is at $(-10^9, 0)$. Then, he will move the circle from $(-10^9, 0)$ to $(10^9, 0)$. Here, he continuously moves the circle so that the boundaries of the passage or the nails do not penetrate the interior of the circle. Find the maximum possible value of $r$ such that it is possible to move the circle to $(10^9, 0)$. ## Constraints * All values in input are integers. * $1 \leq N \leq 100$ * $|x_i|, |y_i| < 100$ * If $i \neq j$, $(x_i, y_i) \neq (x_j, y_j)$. ## 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

2
0 -40
0 40

Output #1

40

![image](https://img.atcoder.jp/ghi/493d8b75d6dd331fcc0f3949f12262b3.jpg)
As shown in the figure, we can move the circle with $r=40$ from $(-10^9, 0)$ to $(10^9, 0)$ by moving it along $y=0$.
When $x=0$, the circle exactly touches the two nails, which is fine since they do not penetrate the interior of the circle.
Any value of $r$ greater than $40$ makes it impossible to move the circle to $(10^9, 0)$, so the maximum possible value is $r=40$.

Input #2

Output #2

50.5

Input #3

Output #3

33.541019662496845446

Input #4

Output #4

35.003571246374276203

API Response (JSON)

{
  "problem": {
    "name": "Silver Woods",
    "description": {
      "content": "On the $xy$\\-plane, we have a passage surrounded by the two lines $y=-100$ and $y=100$. In the part of this passage with $-100 < x < 100$, there are $N$ negligibly small nails. The coordinates of the ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc181_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On the $xy$\\-plane, we have a passage surrounded by the two lines $y=-100$ and $y=100$.\nIn the part of this passage with $-100 < x < 100$, there are $N$ negligibly small nails. The coordinates of the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments