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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<string>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
const ll mod=1e9+7;
ll n,k;
int main(){
  ll n;
  cin>>n;
  vector<ll> v;
  for(int i=0;i<n;i++){
    ll a;
    cin>>a;
    v.push_back(a);
  }
  ll mm=0,ans=0,kans=0;
  for(int i=0;i<n;++i){
    if(v[i]<=mm){
      kans++;
      mm=v[i];
    }
    else{
      ans=max(ans,kans);
      kans=1;
      mm=v[i];
    }
  }
cout<<ans<<endl;
}