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 <bits/stdc++.h>

using namespace std;

typedef long long int lli;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n, a;
    cin >> n;
    vector<int> vec(200000, 0);
    auto ibegin = vec.end();
    for (int i=0; i<n; i++) {
        cin >> a;
        auto itr = lower_bound(ibegin, vec.end(), a);

        if (itr == ibegin) {
            ibegin--;
            *ibegin = a;
        }
        else {
            *itr = a;
        }
    }

    // for (int i=l; i<=r; i++) cout << vec[i] << endl;

    cout << vec.end()-ibegin << endl;

    return 0;
}