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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef long long ll;
typedef long double lld;
typedef long long int lli;
using namespace std;
const int N = 1000001;
const int MOD=1e9+7;
const bool DEBUG = 1;
#define sd(x) scanf("%d", &x)
#define sd2(x, y) scanf("%d%d", &x, &y)
#define sd3(x, y, z) scanf("%d%d%d", &x, &y, &z)
#define endl "\n"
#define fi first
#define se second
#define eb emplace_back
#define fbo find_by_order
#define ook order_of_key
#define pb(x) push_back(x)
#define mp(x, y) make_pair(x, y)
#define LET(x, a) __typeof(a) x(a)
#define foreach(it, v) for (LET(it, v.begin()); it != v.end(); it++)
#define MEMS(a, b) memset(a, b, sizeof(a))
#define _			\
    ios_base::sync_with_stdio(false);			\
    cin.tie(NULL);			\
    cout.tie(NULL);
#define __ 			\
    freopen("input.txt", "r", stdin);			\
    freopen("output.txt", "w", stdout);
#define all(c) c.begin(), c.end()
#define inf 1000000000000000001
#define epsilon 1e-6
#define int ll
#define RUN_T			 \
    int _t; 			 \
    cin >> _t;			 \
    while (_t--)			 
#define tr(...)				\
if (DEBUG) {				\
cout << __FUNCTION__ << ' ' << __LINE__ << " = ";				\
trace(#__VA_ARGS__, __VA_ARGS__);				\
}
template <typename S, typename T>
ostream &operator<<(ostream &out, pair<S, T> const &p) {
    out << '(' << p.fi << ", " << p.se << ')';
    return out;
}
template <typename T>
ostream &operator<<(ostream &out, set<T> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << (*i) << ' ';
    return out;
}
template <typename T, typename V>
ostream &operator<<(ostream &out, map<T, V> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << "\n" << (i->first) <<  ":"  << (i->second);
    return out;
}
template <typename T, typename V>
ostream &operator<<(ostream &out, unordered_map<T, V> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << "\n" << (i->first) <<  ":"  << (i->second);
    return out;
}
template <typename T>
ostream &operator<<(ostream &out, multiset<T> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << (*i) << ' ';
    return out;
}
template <typename T>
ostream &operator<<(ostream &out, unordered_set<T> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << (*i) << ' ';
    return out;
}
template <typename T>
ostream &operator<<(ostream &out, unordered_multiset<T> const &v) {
    for (auto i = v.begin(); i != v.end(); i++)
        out << (*i) << ' ';
    return out;
}
template <typename T> ostream &operator<<(ostream &out, vector<T> const &v) {
    ll l = v.size();
    for (ll i = 0; i < l - 1; i++)
        out << v[i] << ' ';
    if (l > 0)
        out << v[l - 1];
    return out;
}
template <typename T> void trace(const char *name, T &&arg1) {
    cout << name <<  ":"  << arg1 << endl;
}
template <typename T, typename... Args>
void trace(const char *names, T &&arg1, Args &&... args) {
    const char *comma = strchr(names + 1, ',');
    cout.write(names, comma - names) <<  ":"  << arg1 <<  "|" ;
    trace(comma + 1, args...);
}
template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
int gcd(int a, int b) {
     if (b == 0)
        return a;
    return gcd(b, a % b);
}
const int MAXN = (1 << 20);

// template <class T>
struct fenwick
{
	int sz;
	int tr[MAXN];

	void init(int n)
	{
		sz = n + 1;
		memset(tr, 0, sizeof(tr));
	}

	int query(int idx)
	{
		int ans = 0;
		for(; idx >= 1; idx -= (idx & -idx))
			ans = max(ans, tr[idx]);
		return ans;
	}

	void update(int idx, int val)
	{
		if(idx <= 0) return;
		for(; idx <= sz; idx += (idx & -idx))
			tr[idx] = max(tr[idx], val);
	}

	// int query(int l, int r) { return query(r) - query(l - 1); }
};
int32_t main() {
    _
    int n;
    cin >> n; 
    vector<int>h(n),c(n);
    for(int& i: h){
        cin >> i;
    }
    for(int& i: c){
        cin >> i;
    }
    fenwick* sgt = new fenwick();
    sgt->init(n + 1);
    for(int i = 1; i <= n; i++){
        int val = sgt->query(h[i - 1] - 1);
        // tr(val, h[i - 1], c[i - 1]);
        val += c[i - 1];
        sgt->update(h[i - 1], val);
    }
    int ans = sgt->query(n);
    cout << ans << endl;
}