You are given a polyline through
. Compute the minimum length of a vertical segment (parallel to the
-axis) with its bottom endpoint somewhere on the polyline such that from every point on the polyline, the segment is at least partially visible.
Constraints
Input Specification
The first line contains a single integer, .
The next line contains space-separated integers, the
th being
. These will be presented in increasing order.
The next line contains space-separated integers, the
th being
.
Output Specification
Output the desired length to exactly three decimal places.
Sample Input
6
1 2 4 5 6 7
1 2 2 4 2 1
Sample Output
1.000
Comments