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 <algorithm>
#include <cstring>
#include <iostream>
#include <vector>

using namespace std;

int main() {
  int n;
  vector<int> a;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int tmp;
    cin >> tmp;
    a.push_back(tmp);
  }
  vector<int> ans;
  ans.push_back(a[0]);
  for (int i = 1; i < n; i++) {
    auto it = lower_bound(ans.begin(), ans.end(), a[i]);
    if (it != ans.end()) {
      ans.push_back(a[i]);
    } else {
      *(it--) = a[i];
    }
    // sort(ans.begin(), ans.end());
  }
  cout << ans.size() << endl;
  return 0;
}