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 <map>

using namespace std;

int main(){
    map<int, int> mp;
    int N;
    int ans = 0;
    cin >> N;
    mp[-1] = 1;
    for(int i = 0; i < N; i++){
        int A;
        cin >> A;
        auto ptr = mp.lower_bound(A);
        ptr--;
        if(ptr->first == -1){
            //cout << i << endl;
            if(mp.count(A) != 0){
                mp[A]++;
            }else{
                mp[A]=1;
            }
            ans++;
        }else{
            int m = ptr->first;
            mp[m]--;
            if(mp[m] == 0){
                mp.erase(m);
            }
            if(mp.count(A) != 0){
                mp[A]++;
            }else{
                mp[A] = 1;
            }
        }
    }
    cout << ans << endl;
}