B. The Meeting Place Cannot Be Changed
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

Print the minimum time (in seconds) needed for all the n friends to meet at some point on the road.

37 1 31 2 1
2.000000000000
45 10 3 22 3 2 4
1.400000000000