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 <algorithm>
#include <numeric>

using namespace std;

int main(void) {
    int N;
    cin >> N;
    vector<int> A(N);
    for(int i=0; i<N; i++) {
        cin >> A.at(i);
    }
    int color = 0;
    int color_num = 1;
    vector<int> max;
    max.push_back(A.at(0));
    for(int i=1; i<N; i++) {
        if(A.at(i) <= A.at(i-1)) {
            int min_of_max = *min_element(max.begin(), max.end());
            if(A.at(i) <= min_of_max) {
                ++color_num;
                max.push_back(A.at(i));
            } else {
                for(int j=0; j<color_num; j++) {
                    if(max.at(j) < A.at(i)) {
                        color = j;
                        max.at(color) = A.at(i);
                        break;
                    }
                }
            }
        } else {
            max.at(color) = A.at(i);
        }
    }
    cout << color_num << endl;
    return 0;
}