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;cin>>n;
  multiset<int> st;
  for(int i=0;i<n;++i){
    int tmp;cin>>tmp;
    if(st.size()==0 ||tmp <= *st.begin()){
      st.insert(tmp);
    } else {
      auto it = lower_bound(st.begin(),st.end(),tmp);
      it--;
      st.erase(*it);
      st.insert(tmp);     
    }
    /*
    for(auto i:st){
      cout<<i<<" ";
    }cout<<endl;
    */
  }
  cout<<st.size()<<endl;
  return 0;
}