Trick E. Dingo is trying, as usual, to catch his nemesis the Street
Sprinter. His past attempts using magnets, traps and explosives have
failed miserably, so he’s catching his breath to gather observational
data and learn more about how fast Street Sprinter is.

Trick E. Dingo and Street Sprinter both inhabit a single straight
west-east road with a particularly famous rock on it known
affectionately as The Origin. Positions on this straight road are
measured numerically according to the distance from The Origin, and
using negative numbers for positions west of The Origin and positive
numbers for positions east of The Origin.

The observations by Trick E. Dingo each contain two numbers: a time,
and the value of Street Sprinter’s position on the road at that time.
Given this information, what speed must Street Sprinter must be capable
of?

\(2\le N \le 100\ 000\)
\(0 \le T \le 1\ 000\ 000\ 000\)
\(-1\ 000\ 000\ 000 \le X \le 1\ 000\ 000\ 000\)
\(N \le 1000\)

The first line contains a number \(2\le N \le 100\ 000\), the number of observations that follow. The next
\(N\) lines each contain an integer
\(0 \le T \le 1\ 000\ 000\ 000\)
indicating the time, in seconds, of when a measurement was made, and an
integer \(-1\ 000\ 000\ 000 \le X \le 1\ 000\ 000\ 000\) indicating the position, in metres, of the Street
Sprinter at that time. No two lines will have the same value of \(T\).

For 7 of the 15 available marks, \(N \le 1000\).

Output a single number \(X\), such that
we can conclude that Street Sprinter’s speed was at least \(X\) metres/second at some point in time,
and such that \(X\) is as large as
possible. If the correct answer is \(C\), the grader will view \(X\) as correct if \(|X-C|/C < 10^{-5}\).

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출처 CCC 2020 Senior