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 <bits/stdc++.h>
using namespace std;

int main()
{
    int N;
    cin >> N;

    vector<long long> A(N);
    set<long long> s;
    for (int i = 0; i < N; i++)
    {
        cin >> A[i];
    }

    vector<long long> q(1, 10000000000);
    for (int i = 0; i < N; i++)
    {
        if (A[i] <= q.back())
        {
            q.push_back(A[i]);
            continue;
        }
        int l = 0;
        int r = q.size() - 1;
        while (r - l > 1)
        {
            int c = (l + r) / 2;
            if (A[i] > q[c])
            {
                r = c;
            }
            else
            {
                l = c;
            }
        }
        q[r] = A[i];
    }
    cout << q.size() - 1 << endl;
}