E. Skyline Photo
time limit per test
2.5 seconds
memory limit per test
256 megabytes
standard input
standard output

Alice is visiting New York City. To make the trip fun, Alice will take photos of the city skyline and give the set of photos as a present to Bob. However, she wants to find the set of photos with maximum beauty and she needs your help.

There are $$$n$$$ buildings in the city, the $$$i$$$-th of them has positive height $$$h_i$$$. All $$$n$$$ building heights in the city are different. In addition, each building has a beauty value $$$b_i$$$. Note that beauty can be positive or negative, as there are ugly buildings in the city too.

A set of photos consists of one or more photos of the buildings in the skyline. Each photo includes one or more buildings in the skyline that form a contiguous segment of indices. Each building needs to be in exactly one photo. This means that if a building does not appear in any photo, or if a building appears in more than one photo, the set of pictures is not valid.

The beauty of a photo is equivalent to the beauty $$$b_i$$$ of the shortest building in it. The total beauty of a set of photos is the sum of the beauty of all photos in it. Help Alice to find the maximum beauty a valid set of photos can have.


The first line contains an integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$), the number of buildings on the skyline.

The second line contains $$$n$$$ distinct integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$). The $$$i$$$-th number represents the height of building $$$i$$$.

The third line contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$-10^9 \le b_i \le 10^9$$$). The $$$i$$$-th number represents the beauty of building $$$i$$$.


Print one number representing the maximum beauty Alice can achieve for a valid set of photos of the skyline.

1 2 3 5 4
1 5 3 2 4
1 4 3 2 5
-3 4 -10 2 7
2 1
-2 -3
4 7 3 2 5 1 9 10 6 8
-4 40 -46 -8 -16 4 -10 41 12 3

In the first example, Alice can achieve maximum beauty by taking five photos, each one containing one building.

In the second example, Alice can achieve a maximum beauty of $$$10$$$ by taking four pictures: three just containing one building, on buildings $$$1$$$, $$$2$$$ and $$$5$$$, each photo with beauty $$$-3$$$, $$$4$$$ and $$$7$$$ respectively, and another photo containing building $$$3$$$ and $$$4$$$, with beauty $$$2$$$.

In the third example, Alice will just take one picture of the whole city.

In the fourth example, Alice can take the following pictures to achieve maximum beauty: photos with just one building on buildings $$$1$$$, $$$2$$$, $$$8$$$, $$$9$$$, and $$$10$$$, and a single photo of buildings $$$3$$$, $$$4$$$, $$$5$$$, $$$6$$$, and $$$7$$$.