Score : $300$ points

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.

2
3 5 2
4 5

9

If the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.

• The first hero defeats two monsters attacking the first town and two monsters attacking the second town.
• The second hero defeats three monsters attacking the second town and two monsters attacking the third town.

3
5 6 3 8
5 100 8

22

2
100 1 1
1 100

3