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: Wrong Answer)

#include <iostream>
#include <vector>
#include <stack>

int main() {
    int N;
    std::cin >> N;
    std::cin.ignore();
    int n = N;
    std::vector<int> A;
    A.reserve(N);
    while(n-->0){
        int v;
        std::cin >> v;
        A.push_back(v);
        std::cin.ignore();
    }
    std::vector<int> maxvals;
    int color = 1;
    maxvals.push_back(*A.rbegin());
   
    for(auto it = A.rbegin() + 1; it!=A.rend();++it) {
        if(*(it-1) <= *it) {
            if(maxvals.size()==1) {
                maxvals.push_back(*it);
                ++color;
            } else {
                int i = maxvals.size() -2;
                for(; i>0; --i) {
                    if(maxvals[i] > *it) {
                        maxvals.resize(i);
                        break;
                    }
                }

                if(i==0) {
                   maxvals.push_back(*it);
                   ++color;
                }
            }
        } 
    }
    
    std::cout << color << std::flush;
    
}