A10775 | 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.

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.

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.