Byteocircle

Byteocircle is a country of $n$ cities numbered $0$ through $n-1$. Exactly $n-1$ of them lie on a circle, and walking around it you meet cities $1, 2, \ldots, n-1$ in that order. Every two neighbouring cities on the circle are joined by a two-way road. The capital, city $0$, sits at the centre of the circle and has a road to every other city.

The travel time along each road is known. The government wants to make travelling between cities easier, so it will pick the two cities that are farthest apart and build an airport in each of them. The distance between two cities is the travel time of the fastest route from one to the other.

The first line contains the number of cities $n$. ($3 \le n \le 500\,000$)

The second line contains $n-1$ positive integers. The $i$-th of them is the travel time of the road between city $i$ and the next city on the circle. The city that follows city $n-1$ is city $1$.

The third line contains $n-1$ positive integers. The $i$-th of them is the travel time of the road between the capital and city $i$.

The travel times of all roads add up to at most $10^9$.

Print one integer, the travel time between the two farthest cities.

In the example the two farthest cities are city $2$ and city $4$, and the travel time between them is $7$. The airports belong in those two cities.