There are $N$ flowers arranged in a row. For each $i\ (1≤i≤N)$, the height and the beauty of the $i$-th flower from the left is $h_i$ and $a_i$, respectively. Here, $h_1, h_2, \ldots, h_N$ are all distinct.
Taro is pulling out some flowers so that the following condition is met:

• The heights of the remaining flowers are monotonically increasing from left to right.

Find the maximum possible sum of the beauties of the remaining flowers.

Input is given from Standard Input in the following format:
$N$
$h_1\ h_2\ \ldots\ h_N$
$a_1\ a_2\ \ldots\ a_N$

Print the maximum possible sum of the beauties of the remaining flowers.

All values in input are integers.
$1 \leq N \leq 2 × 10^5$
$1 \leq h_i \leq N$
$h_1, h_2, \ldots, h_N$ are all distinct.
$1 \leq a_i \leq 10^9$

60

We should keep the second and fourth flowers from the left. Then, the heights would be 1, 2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.

31

We should keep the second, third, sixth, eighth and ninth flowers from the left.