You are given \(N\) destinations that must be covered in \(N\) days in any order. Any \(i^{th}\) (\(1\le i\le N\)) destination can be traveled on any \(j^{th}\ (1\le j\le N)\) day. There are only two ways to reach any destination and that is by cars or buses. The cost of reaching to the \(i^{th}\) destination by cars _{\((C_1,C_2,.....C_n)\)} and buses _{\((B_1, B_2,.....B_n)\)} are given.

The only constraint is that you cannot use the same way of travel on two consecutive days. Determine the minimum total cost that you need to pay in reaching all \(N\) destinations.

Input format

First line: A single integer \(N\)
Second line: \(N\) space-separated integers denoting the cost of reaching the destination by cars
Third line: \(N\) space-separated integers denoting the cost of reaching the destination by buses

Output format

Print the minimum total cost that you need to pay in reaching all \(N\) destinations.

Constraints

\(1\le N \le10^5\\ 1\le C_i,\ B_i \le10^9\)