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;

#define rep(i, n) for (int i = (int)(0); i < (int)(n); ++i)
using ll = long long;

signed main()
{
  int n; cin>>n;
  vector<int> a(n);
  rep(i,n) cin>>a[i];
  deque<int> d;
  rep(i,n){
    int p = lower_bound(d.begin(),d.end(),a[i]) - d.begin(); // a[i]以上の最小値が登場するインデックス
    if(p==0){
      d.push_front(a[i]);
    }else d[p-1]=a[i];
  }
  int ans=d.size();
  cout<<ans<<endl;
}