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;
 
int main(){ 
  int N;
  vector<int64_t> A(100010, -1);

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

  
  vector<int64_t> cur_max; cur_max.push_back(A[0]);
  int ans = 1; 

  for(int i=1; i<N; i++){
    sort(cur_max.begin(), cur_max.end());
    
    if(A[i] <= cur_max[0]){
      cur_max.push_back(A[i]);
      ans++;
    } else {
      int p = upper_bound(cur_max.begin(), cur_max.end(), A[i]) - cur_max.begin();
      cur_max[p] = A[i];
    }    
  }

  cout << ans << endl;

}