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

int check(vector<int> x){
  int k=x.size();
  for(int i=0;i<k;i++){
    if(x.at(i)==0){
      return 0;
    }
  }
  return 1;
}
int main(){
  int N; cin >> N;
  vector<int> MY(N);
  for(int i=0;i<N;i++){
    cin >> MY.at(i);
  }
  vector<int> gard(N,0);
  gard.at(0)=1;
  int now=0;
  int restart=0;
  int count=0;
  int start=0;
  while(true){
    if(check(gard)==1){
      break;
    }
     start=restart;
    restart=N;
    now=MY.at(start);
    if(start==N-1){
      count++;
      break;
    }
  for(int i=start+1;i<N;i++){
    gard.at(start)=1;
    if(gard.at(i)==0){
      if(now<MY.at(i)){
        gard.at(i)=1;
        now=MY.at(i);
      }
      else if(restart>i){
        restart=i;
      }
    }
  }
    count++;
  }
  cout << count << endl;
}