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.IO;

namespace Contest
{
    class SegTree<T>
    {
        private readonly T[] Array;
        private readonly Comparison<T> Compare;
        private readonly int N;
        private readonly T Max;
        public SegTree(int size, T max) : this(size, Comparer<T>.Default, max) { }
        public SegTree(int size, IComparer<T> comparer, T max) : this(size, comparer.Compare, max) { }
        public SegTree(int size, Comparison<T> comparison, T max)
        {
            Max = max;
            N = 1;
            while (N < size)
            {
                N *= 2;
            }
            Compare = comparison;
            Array = new T[2 * N];
            for (int i = 1; i < 2 * N; i++)
            {
                Array[i] = max;
            }
        }

        new public T this[int i]
        {
            get { return Array[i + N]; }
            set { Update(value, i); }
        }


        private T Min(T x, T y)
        {
            return Compare(x, y) < 0 ? x : y;
        }

        public void Update(T item, int index)
        {
            index += N;
            Array[index] = item;
            while (index > 1)
            {
                index /= 2;
                Array[index] = Min(Array[index * 2], Array[index * 2 + 1]);
            }
        }

        private T Q(int left, int right, int k, int l, int r)
        {
            if (left <= l && r <= right)
            {
                return Array[k];
            }
            if (r <= left || right <= l)
            {
                return Max;
            }
            return Min(Q(left, right, k * 2, l, (l + r) / 2), Q(left, right, k * 2 + 1, (l + r) / 2, r));
        }

        public T Query(int left, int right)
        {
            return Q(left, right, 1, 0, N);
        }

    }
    class Program
    {
        private Scanner sc;
        private int N;
        private int[] H;
        private long[] A;
        public void Solve()
        {
            sc = new Scanner();
            N = sc.NextInt();
            H = sc.IntArray();
            A = sc.LongArray();

            var st = new SegTree<long>(N + 1, (a, b) => -a.CompareTo(b), long.MinValue);
            st[0] = 0;
            for (int i = 0; i < N; i++)
            {

                st[H[i]] = st.Query(0, H[i]) + A[i];
            }
            Console.WriteLine(st.Query(0, N + 1));
        }


        static void Main() => new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _stream = new StreamReader(Console.OpenStandardInput());
        _pos = 0;
        _line = new string[0];
        _separator = ' ';
    }
    private readonly char _separator;
    private readonly StreamReader _stream;
    private int _pos;
    private string[] _line;
    #region get a element
    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = _stream.ReadLine().Split(_separator);
            _pos = 0;
        }
        return _line[_pos++];
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    #endregion
    #region convert array
    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }
    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }
    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }
    #endregion
    #region get array
    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = _stream.ReadLine().Split(_separator);
        _pos = _line.Length;
        return _line;
    }
    public int[] IntArray()
    {
        return ToIntArray(Array());
    }
    public long[] LongArray()
    {
        return ToLongArray(Array());
    }
    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }
    #endregion
}