Lying From You

You are given $n$ lines on the plane, each defined by an equation of the form $y = a_i x + b_i$. Changing the coefficients of one line from $(a, b)$ to $(a', b')$ costs $|a - a'| + |b - b'|$ rubles. You can perform this operation any number of times on any lines, and the new coefficients can be any real numbers. The goal is to make all the lines pass through a single point.

Let $C$ be the set of total costs of operations that achieve the goal. Find $\inf C$, the greatest lower bound on the total cost.

The first line contains a positive integer $n$ ($1 \le n \le 10^5$), the number of lines.

Each of the next $n$ lines contains two integers $a_i$ and $b_i$ ($|a_i|, |b_i| \le 10^6$).

Print the answer on a single line with absolute or relative error no more than $10^{-6}$.

In the first example, it is enough to change $b$ of the first line to $-0.5$.