You are given $n$ distinct points $P_1, P_2, \ldots, P_n$ on the coordinate plane, none of which lie on the $x$-axis ($x$-axis is the set of points whose $y$ coordinate is $0$). Let $S$ be the set of all points $X$ on the $x$-axis such that there exist two integers $i, j$ with $1 \le i < j \le n$ such that $XP_i = XP_j$. In other words, $S$ is the set of all points on the $x$-axis which are equidistant from some two distinct points from $P_1, \ldots, P_n$. Find the largest distance between any two points in $S$ (not necessarily distinct). It's guaranteed that in all test cases, $S$ is nonempty and finite. \InputFile The first line contains a single integer $n$ ($2 \le n \le 200000$) --- the number of points. The $i$-th of the next $n$ lines contains two integers $x_i, y_i$ ($-10^9 \le x_i, y_i \le 10^9$, $y_i \neq 0$) --- $x$ and $y$ coordinates of point $P_i$. It's guaranteed that $S$ is nonempty and finite in all testcases. \OutputFile Output a single number --- the largest distance between any two points in $S$ (not necessarily distinct). Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$. Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is accepted if and only if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$. \Note In the sample, $S = \{(-7, 0), (0, 0), (7, 0)\}$. Note that if $S$ contains a single point, the answer will be $0$.