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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <algorithm>
#include <bitset>
#include <tuple>
#include <set>
#include <map>
#define range(i, r) for(int i=0;i<r;i++)
#define ranges(i, l, r) for(int i=l;i<r;i++)
#define vv(a, b, c, d) vector<vector<d> >(a, vector<d>(b, c))
#define vvi std::vector<std::vector<int> >
#define vvl std::vector<std::vector<ll> >
#define MODs 1000000007;
#define MODn 1000000009;
typedef long long int ll;
using namespace std;

int main(int argc, char const *argv[]) {
  int N;
  std::cin >> N;
  std::vector<int> A(N+1);
  multiset<int> num;
  for(int i=1;i<=N;i++) {
    std::cin >> A[i];
  }
  num.insert(A[1]);
  for(int i=2;i<=N;i++){
    if(A[i]<=*num.begin()){
      num.insert(A[i]);
    }else{
      auto itr = lower_bound(num.begin(), num.end(),A[i]);
      itr--;
      num.erase(itr);
      num.insert(A[i]);
    }
  }
  std::cout << num.size() << '\n';
  return 0;
}