Farm Village

There is a village along a road. The village has $N$ houses, numbered 1 to $N$ in order along the road. Each house has a field that can grow up to two units of the crop, and each house needs exactly one unit. The total cost of giving every house one unit of the crop is the sum of the carrying costs and the growing costs.

• Carrying cost: carrying one unit of the crop between house $i$ and house $i+1$ costs $d_i$. The cost is the same in either direction.
• Growing cost: growing one unit of the crop in the field of house $i$ costs $g_i$.

Compute the minimum total cost of supplying one unit of the crop to every house.

The input is a single test case in the following format.

N
d1 d2 ... dN-1
g1 g2 ... gN

The first line contains an integer $N$ ($2 \le N \le 200{,}000$), the number of houses. The second line contains $N-1$ integers separated by spaces. The $i$-th integer $d_i$ ($1 \le d_i \le 10^9$, $1 \le i \le N-1$) is the carrying cost between house $i$ and house $i+1$. The third line contains $N$ integers separated by spaces. The $i$-th integer $g_i$ ($1 \le g_i \le 10^9$, $1 \le i \le N$) is the growing cost of the field of house $i$.

Print the minimum cost of supplying one unit of the crop to every house.