There are $n$ days. On $i^{th}$ day, Marisa can visit Alice Margatroid for $A_i$ happiness, or visit Patchouli Knowledge for $B_i$ happiness. But if she visits one person for 3 or more consecutive days, the other person will get jealous.
What is the maximum amount of happiness she can get after $n$ days, without making anyone jealous?
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
- The third line contains $n$ integers $B_i$.
### Output
- Print the maximum amount of happiness Marisa can obtain.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i, B_i \le 10^9$.
### Example
Input:
```
4
4 4 4 1
1 1 1 4
```
Output:
```
13
```
