The Meeting Place Cannot Be Changed

题意翻译

在一条直线上站在 $n$ 个朋友，第 $i$ 个朋友的位置为 $X_i$ ,并且可以以不超过 $V_i$ 每秒的任意速度向左或者向右移动。请计算最少需要多少秒，所有的 $n$ 个朋友可以在同一个位置汇合。注意最后的汇合点不一定是整数点。 Translated by @P指向NULL

题目描述

The main road in Bytecity is a straight line from south to north. Conveniently, there are coordinates measured in meters from the southernmost building in north direction. At some points on the road there are $ n $ friends, and $ i $ -th of them is standing at the point $ x_{i} $ meters and can move with any speed no greater than $ v_{i} $ meters per second in any of the two directions along the road: south or north. You are to compute the minimum time needed to gather all the $ n $ friends at some point on the road. Note that the point they meet at doesn't need to have integer coordinate.

输入输出格式

输入格式

The first line contains single integer $ n $ ( $ 2<=n<=60000 $ ) — the number of friends. The second line contains $ n $ integers $ x_{1},x_{2},...,x_{n} $ ( $ 1<=x_{i}<=10^{9} $ ) — the current coordinates of the friends, in meters. The third line contains $ n $ integers $ v_{1},v_{2},...,v_{n} $ ( $ 1<=v_{i}<=10^{9} $ ) — the maximum speeds of the friends, in meters per second.

输出格式

Print the minimum time (in seconds) needed for all the $ n $ friends to meet at some point on the road. Your answer will be considered correct, if its absolute or relative error isn't greater than $ 10^{-6} $ . Formally, let your answer be $ a $ , while jury's answer be $ b $ . Your answer will be considered correct if  holds.

输入输出样例

输入样例 #1

3
7 1 3
1 2 1

输出样例 #1

2.000000000000

输入样例 #2

4
5 10 3 2
2 3 2 4

输出样例 #2

1.400000000000

说明

In the first sample, all friends can gather at the point $ 5 $ within $ 2 $ seconds. In order to achieve this, the first friend should go south all the time at his maximum speed, while the second and the third friends should go north at their maximum speeds.

题意翻译

在一条直线上站在 $n$ 个朋友，第 $i$ 个朋友的位置为 $X_i$ ,并且可以以不超过 $V_i$ 每秒的任意速度向左或者向右移动。请计算最少需要多少秒，所有的 $n$ 个朋友可以在同一个位置汇合。注意最后的汇合点不一定是整数点。 Translated by @P指向NULL