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: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef pair<ll,ll> P;
typedef vector<P> vp;
typedef vector<string> vs;
typedef vector<bool> vb;

const ll mod=1e9+7;
const ll inf=1e16;

#define rep(i,m,n) for(ll i=m;i<n;i++)
#define repr(i,m,n) for(ll i=m-1;i>=n;i--)
#define fi first
#define se second
#define chmax(x,y) x=max(x,y)
#define chmin(x,y) x=min(x,y)
#define eb(x) emplace_back(x)
#define all(x) x.begin(),x.end()
#define gll greater<ll>()


ll n;
vll a;
 
void solve(){
 cin >> n;
 a.resize(n);
 rep(i,0,n) cin >> a[i];
 vll d;
 rep(i,0,n){ 
  auto it=lower_bound(d.rbegin(),d.rend(),a[i]);
  if(it==d.rbegin()){
    d.eb(a[i]);
  }else{
   --it;
   *it=a[i]; 
    
  }
   
 }
  cout << d.size() << endl;
}

int main(){
   cin.tie(nullptr);
  ios::sync_with_stdio(false);
  solve();
}