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.

Sample Input 1

2
3 5 2
4 5

Sample Output 1

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.

Sample Input 2

3
5 6 3 8
5 100 8

Sample Output 2

22

Sample Input 3

2
100 1 1
1 100

Sample Output 3

3