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 (Clang 3.8.0) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<map>
#include<deque>

using namespace std;

int main(){
    int N; cin >> N;
    deque<int> q;
    for (int i = 0; i < N; i++){
        int a_i; cin >> a_i;
        if (i == 0){
            q.push_back(a_i);
            continue;
        }
        auto itr = lower_bound(q.begin(), q.end(), a_i);
        if (itr == q.begin()) q.push_front(a_i);
        else{
            --itr;
            *itr = a_i;
        }
    }
    cout << q.size() << endl;
}