Problem:
Score : 100 points

Problem Statement

There are N flowers arranged in a row.
For each i (1 \leq i \leq 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.

Constraints

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

Input

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

Output

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

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.

Sample Input 2

1
1
10

Sample Output 2

10

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

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

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

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var num = Input.num;
        var hs = Input.ar;
        var ar = Input.ar;
        Func<long, long, long> func = (long a, long b) => Max(a, b);
        var dp = new SegmentTree<long>(num+1, 0, func, func);
        for (var i = 0; i < num; i++)
            dp.Update(hs[i], dp.Query(0, hs[i]) + ar[i]);
        WriteLine(dp.Query(0, num + 1));
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        return default(T);
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class SegmentTree<T>
{
    private List<T> item;
    private int _num;
    private Func<T, T, T> _func;
    private Func<T, T, T> updateFunc;
    private T _init;

    private int Parent(int index)
        => (index - 1) / 2;
    private int Left(int index)
        => 2 * index + 1;
    private int Right(int index)
        => 2 * (index + 1);

    public SegmentTree(int num, T init, Func<T, T, T> func, Func<T, T, T> updateFunc = null)
    {
        _func = func;
        _num = 1;
        _init = init;
        this.updateFunc = updateFunc ?? ((T val1, T val2) => val2);
        while (_num < num)
            _num *= 2;
        item = new List<T>(2 * _num - 1);
        for (var i = 0; i < 2 * _num - 1; i++)
            item.Add(init);
    }
    public void Update(int index, T value)
    {
        index += _num - 1;
        item[index] = updateFunc(item[index], value);
        while (index > 0)
        {
            index = Parent(index);
            item[index] = _func(item[Left(index)], item[Right(index)]);
        }
    }
    public T Query(int left, int right)
        => Query(left, right, 0, 0, _num);
    public T Query(int left, int right, int k, int l, int r)
    {
        if (r <= left || right <= l) return _init;
        if (left <= l && r <= right) return item[k];
        else
            return _func(Query(left, right, Left(k), l, (l + r) / 2), Query(left, right, Right(k), (l + r) / 2, r));
    }
}