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>
#include <iomanip>
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define fi first
#define se second
#define mp make_pair
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;

ll N,M,H,W,K,A,B,L;
string alpha = "abcdefghijklmnopqrstuvwxyz";
string ALPHA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const ll MOD = (1e+9) + 7;

int main() {
    cin>>N;
    vec a(N);
    rep(i,N) cin>>a[i];
    multiset<ll> mset;
    rep(i,N){
        auto ite = mset.lower_bound(a[i]);
        if(ite == mset.begin()){
            mset.insert(a[i]);
        }else{
            --ite;
            mset.erase(ite);
            mset.insert(a[i]);
        }
    }
    cout<<mset.size()<<endl;
}