p02959 AtCoder Beginner Contest 135 - City Savers
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.

Examples

Input

2
3 5 2
4 5


Output

9


Input

3
5 6 3 8
5 100 8


Output

22


Input

2
100 1 1
1 100


Output

3
```python
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

res = 0
for n in range(N):
    b = min(A[n], B[n])
    B[n] -= b
    b2 = min(A[n + 1], B[n])
    A[n + 1] -= b2
    res += b + b2

print(res)

```