Quick Gathering

Problem Description

There are $n$ people on a number line, and they want to gather at a single point. The $i$-th person starts at position $a_i$ and can move at most $b_i$ units per second. What is the minimum time needed for all $n$ people to gather at some point?

Input Format

The first line contains an integer $n$.

The following $n$ lines each contain two integers $a_i, b_i$.

Output Format

Output one number: the answer. It is accepted if the relative or absolute error is within $10^{-6}$.

Sample Input

2
1 2
5 2

Sample Output

1.0000000000

Constraints

For $100\%$ of the data, $1 \leq n \leq 100000, 1 \leq a_i, b_i \leq 100000$.