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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)| ≤ L · |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:
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.
3 1 1 2 2 3 4
2 1 4 2 2
4 -10 6.342 -7 3 46 18.1 2 -34