Problem F
Lipschitz Constant
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:
\[ f(x)  f(y) \leq L \cdot x  y. \]Input
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.
Output
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 

3 1 1 2 2 3 4 
2 
Sample Input 2  Sample Output 2 

2 1 4 2 2 
2 
Sample Input 3  Sample Output 3 

4 10 6.342 7 3 46 18.1 2 34 
4.111111111 