Problem Statement

Given is an undirected graph with N+1 vertices.
The vertices are called Vertex $0, Vertex 1, \ldots, Vertex N$.
For each $i=1,2,\ldots,N$, the graph has an undirected edge with a weight of A_i connecting Vertex 0 and Vertex i.
Additionally, for each $i=1,2,\ldots,N$, the graph has an undirected edge with a weight of B_i connecting Vertex i and Vertex i+1. (Here, Vertex N+1 stands for Vertex 1.)
The graph has no edge other than these 2N edges above.
Let us delete some of the edges from this graph so that the graph will be bipartite.
What is the minimum total weight of the edges that have to be deleted?

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \dots A_N$
$B_1 B_2 \dots B_N$

Output

Print the answer.

Constraints

• $3 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• $1 \leq B_i \leq 10^9$
• All values in input are integers.

Sample Input 1

5
31 4 159 2 65
5 5 5 5 10

Sample Output 1

16

Deleting the edge connecting Vertices 0,2 (weight: 4), the edge connecting Vertices 0,4 (weight: 2), and the edge connecting Vertices 1,5 (weight: 10) makes the graph bipartite.

Sample Input 2

4
100 100 100 1000000000
1 2 3 4

Sample Output 2

10

见题面 Input 部分

见题面 Output 部分