Grounding the Antennas

There are $N$ antennas positioned along a straight line at distinct integer coordinates $x_1 < x_2 < \cdots < x_N$.

A grounding system may contain either of the following connections:

• Antenna $i$ may be connected directly to the ground at cost $A_{i}$.
• Two antennas $i$ and $j$ may be connected by a cable at cost $|x_{i} - x_{j}|$.

An antenna is considered grounded if it is connected, possibly through other antennas and cables, to at least one antenna that is directly connected to the ground.

Determine the minimum total cost required to ground all $N$ antennas.

The first line contains an integer $N$. ($1 \le N \le 200\,000$)

The second line contains $N$ integers $x_1,x_2,\ldots,x_N$, listed in strictly increasing order. ($0 \le x_1 < x_2 < \cdots < x_N \le 10^{9}$)

The third line contains $N$ integers $A_1,A_2,\ldots,A_N$, where $A_i$ is the cost of grounding antenna $i$ directly. ($1 \le A_i \le 10^{9}$)

Output one integer: the minimum total cost required to ground every antenna.