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 <bits/stdc++.h>
using namespace std;
using ll = long long;

int main()
{
    ios_base::sync_with_stdio(false); cin.tie(NULL);
    int N; cin >> N;
    multiset<int> ms;
    for (int i = 0; i < N; i++) {
        int ai; cin >> ai;
        auto it = ms.lower_bound(ai);
        if (it == ms.begin()) {
            ms.insert(ai);
        }
        else {
            --it;
            ms.erase(it);
            ms.insert(ai);
        }
    }
    cout << ms.size() << '\n';
}