You are given a polyline $(x_1,y_1)$ through $(x_N,y_N)$. Compute the minimum length of a vertical segment (parallel to the $y$-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

$1\le N\le 300$

$|x_i|,|y_i|\le {10}^6$

Input Specification

The first line contains a single integer, $N$.

The next line contains $N$ space-separated integers, the $i$th being $x_i$. These will be presented in increasing order.

The next line contains $N$ space-separated integers, the $i$th being $y_i$.

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