Today you are doing your calculus homework, and you are tasked with finding a Lipschitz constant for a function f(x), which is defined for $N$ integer numbers $x$ and produces real values. Formally, the Lipschitz constant for a function f is the smallest real number $L$ such that for any $x$ and $y$ with f(x) and f(y) defined we have:
\[ |f(x) - f(y)| \leq L \cdot |x - y|. \]The first line contains $N$ – the number of points for which f is defined. The next $N$ lines each contain an integer $x$ and a real number $z$, which mean that $f(x) = z$. Input satisfies the following constraints:
$2 \leq N \leq 200\, 000$.
All $x$ and $z$ are in the range $-10^9 \leq x,z \leq 10^9$.
All $x$ in the input are distinct.
Print one number – the Lipschitz constant. The result will be considered correct if it is within an absolute error of $10^{-4}$ from the jury’s answer.
Sample Input 1 | Sample Output 1 |
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3 1 1 2 2 3 4 |
2 |
Sample Input 2 | Sample Output 2 |
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2 1 4 2 2 |
2 |
Sample Input 3 | Sample Output 3 |
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4 -10 6.342 -7 3 46 18.1 2 -34 |
4.111111111 |