Cute Panda

There are $n$ pandas numbered from $1$ to $n$, and the $i$-th panda has $a_i$ donuts. There are also $n$ bins numbered from $1$ to $n$, and the $i$-th bin can hold up to $b_i$ donuts. For every $i$ from $1$ to $n$, the $i$-th panda can distribute his donuts between the $i$-th bin and the $(i \bmod n + 1)$-th bin.

Find the maximum number of donuts that can be distributed.

The input contains zero or more test cases, and is terminated by end-of-file. Each test case is given as follows.

The first line contains an integer $n$ ($3 \le n \le 10^6$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($0 \le b_i \le 10^9$).

The sum of all $n$ over all test cases does not exceed $10^6$.

For each test case, output one integer: the maximum number of donuts that can be distributed.