Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#define ll long long

using namespace std;

int main () {
    ll n;
    cin >> n;
    multiset <ll> se;

    vector <ll> vec (n);
    for(ll i = 0; i < n; i++)
    {
        cin >> vec[i];
    }

    for(ll i = 0; i < n; i++)
    {
        ll cur = vec[i];
        auto itr = se.lower_bound(cur);

        if(itr != se.begin())
        {
            se.erase(--itr);
        }
        se.insert(cur);
    }
    cout << se.size() << endl;
    return  0 ;
}