24244번 - 100 meter dash 스페셜 저지다국어

문제

As CS student we sit around all day looking at screens. This is bad for us in many different ways; back pain, need of glasses, and lack of social life. According to the government regular exercise can help with some of these problems. Although you strongly believe this might not be the case, you have decided to start running, and tracking your runs with Ztrawa GPS-tracking mobile app.

Ztrawa stores your position coordinates $(x, y)$ at some random intervals. When you are done with your run you can look at many different cool stats like your elevation gain, your fastest 100ドル$m, and your average speed from point $A$ to $B$.

Since all CS students are looking to Min-Max everything you are only interested in your best 100ドル$m over your run. Sadly your Ztrawa app has a bug and the Min-Max feature has stop working, so you need to work it out yourself.

As Ztrawa only collect some finite amount of data points, we will assume constant speed between two consecutive data points. For example, say you were running around a 400ドル$m track and recorded 6ドル$ data points going all around the track and back where you started. This is sample case 1ドル,ドル where we started running from the bottom left, and went around counter-clockwise.

You need to create your own program so you can find what your fastest 100ドル$m was measured in seconds.

Illustration of sample case 1ドル$.

입력

The first line contains an integer 1ドル \leq n \leq 10^5$ indicating the number of readings from Ztrawa. Then follows $n$ lines containing the information of each reading. The $i^{\text{th}}$ such lines contains three real numbers $x_i,ドル $y_i$ and $t_i,ドル indicating that at the time of reading $i,ドル you were at meter coordinates $(x_i, y_i)$ relative to where you started, and $t_i$ seconds has passed since the beginning of the session. It holds that $-10^5 \leq x_i, y_i \leq 10^5$ for every $i,ドル and 0ドル < t_1 < t_2 < \ldots < t_n \leq 10^7$. All real numbers are given with at most 6ドル$ decimal places.

You always start running from $(0, 0)$ at time 0ドル$.

출력

Output a single real number, how fast you ran the fastest 100m measured in seconds. Anything with an absolute or relative error of 10ドル^{-4}$ will be accepted.

제한

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