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: Time Limit Exceeded)

#include <algorithm>
#include <cmath>
#include <iostream>
#include <string>
#include <tuple>
#include <vector>

using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef vector<vi> vvi;

#define INF (1e9)

int N;

int main() {
    cin >> N;

    vi A(N);
    for (int i = 0; i < N; i++) {
        cin >> A[i];
    }

    vi B(0);
    for (int i = 0; i < N; i++) {
        auto it = upper_bound(B.begin(), B.end(), -A[i]);
        if (it != B.end()) {
            // B[it] > -A[i]
            B.erase(it);
        }
        B.push_back(-A[i]);
        sort(B.begin(), B.end());
    }

    cout << B.size() << endl;
    return 0;
}