CF780B.The Meeting Place Cannot Be Changed

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.

字节城的主干道是一条从南到北的直线。方便起见，坐标以米为单位，从最南端的建筑物开始向北测量。

在道路的某些位置上有 $n$ 位朋友，其中第 $i$ 位朋友站在 $x_i$ 米处，并能以任意不超过 $v_i$ 米/秒的速度沿道路向南或向北移动。

你需要计算让所有 $n$ 位朋友在道路某一点（该点坐标不必为整数）会合所需的最短时间。

The first line contains single integer n (2 ≤ n ≤ 60 000) — the number of friends.

The second line contains n integers _x_1, _x_2, ..., x__n (1 ≤ x__i ≤ 109) — the current coordinates of the friends, in meters.

The third line contains n integers _v_1, _v_2, ..., v__n (1 ≤ v__i ≤ 109) — the maximum speeds of the friends, in meters per second.

第一行包含一个整数 $n$（$2 \leq n \leq 60\,000$）——朋友的数量。

第二行包含 $n$ 个整数 $x_1,\,x_2,\,...,\,x_n$（$1 \leq x_i \leq 10^9$）——朋友们当前的坐标（单位：米）。

第三行包含 $n$ 个整数 $v_1,\,v_2,\,...,\,v_n$（$1 \leq v_i \leq 10^9$）——朋友们的最大速度（单位：米/秒）。

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.

输出所有 $n$ 位朋友在道路某一点相遇所需的最短时间（单位：秒）。

若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。形式化地，设你的答案为 $a$，评测组的答案为 $b$。当且仅当 成立时，你的答案被视为正确。

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.

在第一个样例中，所有朋友都可以在 2 秒内聚集到点 5。为实现这一点，第一位朋友应始终以最大速度向南移动，而第二位和第三位朋友则应以各自的最大速度向北移动。