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