There are flowers arranged in a row. For each , the height and the beauty of the -th flower from the left is and , respectively. Here, 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.

#### Constraints

- All values in input are integers.
- are all distinct.

#### Input Specification

The first line will contain the integer .

The next line will contain integers, .

The next line will contain integers, .

#### Output Specification

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

#### Sample Input 1

```
4
3 1 4 2
10 20 30 40
```

#### Sample Output 1

`60`

#### Explanation For Sample 1

We should keep the second and fourth flowers from the left. Then, the heights would be from left to right, which is monotonically increasing, and the sum of the beauties would be .

#### Sample Input 2

```
1
1
10
```

#### Sample Output 2

`10`

#### Explanation For Sample 2

The condition is met already at the beginning.

#### Sample Input 3

```
5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000
```

#### Sample Output 3

`5000000000`

#### Explanation For Sample 3

The answer may not fit into a 32-bit integer type.

#### Sample Input 4

```
9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5
```

#### Sample Output 4

`31`

#### Explanation For Sample 4

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

## Comments

This is similar to longest increasing subsequence

It isn't mentioned here, but assuming the randomly generated test data complies with the original problem's constraints, . In other words, the heights form a permutation of the integers from to .

https://atcoder.jp/contests/dp/tasks/dp_q