Problem Statement

There are $N$ monsters along a number line. At the coordinate $i$ $(1\leq i\leq N)$ is a monster with a stamina of $A_i$. Additionally, at the coordinate $i$, there is a permanent shield of a strength $B_i$. This shield persists even when the monster at the same coordinate has a health of $0$ or below.

Takahashi, a magician, can perform the following operation any number of times.

• Choose integers $l$ and $r$ satisfying $1\leq l\leq r\leq N$.
• Then, consume $\max(B_l, B_{l+1}, \ldots, B_r)$ MP (magic points) to decrease by $1$ the stamina of each of the monsters at the coordinates $l,l+1,\ldots,r$.

When choosing $l$ and $r$, it is fine if some of the monsters at the coordinates $l,l+1,\ldots,r$ already have a stamina of $0$ or below. Note, however, that the shields at all those coordinates still exist.

Takahashi wants to make the stamina of every monster $0$ or below. Find the minimum total MP needed to achieve his objective.

Constraints

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

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N

Output

Print the minimum total MP needed to achieve his objective.