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 System.IO;
using SB = System.Text.StringBuilder;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<long, long>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    void chmax<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? b : a; }
    void chmin<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? a : b; }

    void solve()
    {
        int N = cin.nextint;
        var H = cin.scanint;
        var A = cin.scanlong;

        var G = new SegTree<long>(N + 1, merge, long.MinValue);
        G.update(0, 0);
        for (int i = 0; i < N; i++)
        {
            var height = G.run(0, H[i]);
            //WriteLine(height);
            G.update(H[i], height + A[i]);
        }
        WriteLine(G.run(0, N));
    }

    static long merge(long a, long b)
    {
        return Max(a, b);
    }
}

class SegTree<T>
{
    readonly int n;
    int s, t;
    T[] tr;
    readonly Func<T, T, T> f;
    readonly T exnum;

    /// <summary>
    ///  セグメントツリーの構築1
    /// </summary>
    /// <param name="m">要素数</param>
    /// <param name="f">マージ関数</param>
    /// <param name="ex">単位元</param>
    public SegTree(int m, Func<T, T, T> f, T ex)
    {
        this.f = f; exnum = ex; n = 1;
        while (n < m) n <<= 1;
        tr = new T[(n << 1) - 1];
        for (int i = 0; i < tr.Length; i++) tr[i] = ex;
    }
    /// <summary>
    /// セグメントツリーの構築2
    /// </summary>
    /// <param name="m">要素数</param>
    /// <param name="f">マージ関数</param>
    /// <param name="ex">単位元</param>
    /// <param name="ini">初期値 <typeparamref name="T"/>? </param>
    public SegTree(int m, Func<T, T, T> f, T ex, T ini) : this(m, f, ex)
    {
        for (int i = 0; i < m; ++i) assign(i, ini);
        all_update();
    }
    /// <summary>
    /// セグメントツリーの構築3
    /// </summary>
    /// <param name="m">要素数</param>
    /// <param name="f">マージ関数</param>
    /// <param name="ex">単位元</param>
    /// <param name="ini">初期値 IList<typeparamref name="T"/>? </param>
    public SegTree(int m, Func<T, T, T> f, T ex, IList<T> ini) : this(m, f, ex)
    {
        for (int i = 0; i < m; ++i) assign(i, ini[i]);
        all_update();
    }
    /// <summary>
    /// 最下層に値の代入
    /// </summary>
    /// <param name="j">代入するインデックス</param>
    /// <param name="x">代入する値</param>
    public void assign(int j, T x) => tr[j + n - 1] = x;
    public void update(int j, T x)
    {
        assign(j, x);
        update(j);
    }
    public void update(int j)
    {
        int i = j + n - 1;
        while (i > 0) { i = i - 1 >> 1; tr[i] = f(tr[i << 1 | 1], tr[i + 1 << 1]); }
    }
    public void all_update() { for (int i = n - 2; i >= 0; i--) tr[i] = f(tr[i << 1 | 1], tr[i + 1 << 1]); }
    public T look(int j) => tr[j + n - 1];

    ///<summary>return node[s, t]</summary>
    public T run(int s, int t) { t++; this.s = s; this.t = t; return q(0, 0, n); }
    T q(int k, int l, int r) => r <= s || t <= l ? exnum : s <= l && r <= t ? tr[k]
                              : f(q(k << 1 | 1, l, l + r >> 1), q(k + 1 << 1, l + r >> 1, r));
}   
class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f;
    public U s;
    public Pair(T f, U s)
    {
        this.f = f;
        this.s = s;
    }
    public int CompareTo(Pair<T, U> a)
    {
        return f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    }
    public override string ToString()
    {
        return $"{f} {s}";
    }
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values) { WriteLine(string.Join(" ", values)); }
    public static string join<T>(this IEnumerable<T> values, string sep) { return string.Join(sep, values); }
    public static string concat<T>(this IEnumerable<T> values) { return string.Concat(values); }
    public static string reverse(this string s) { return s.Reverse().concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count();
        int mid;

        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count();
        int mid;

        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}