Problem Statement

There are $N+1$ towns. The $i$-th town is being attacked by $A_i$ monsters.

We have $N$ heroes. The $i$-th hero can defeat monsters attacking the $i$-th or $(i+1)$-th town, for a total of at most $B_i$ monsters.

What is the maximum total number of monsters the heroes can cooperate to defeat?

Constraints

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

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N

Output

Print the maximum total number of monsters the heroes can defeat.