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 <cmath>
#include <string>
#include <vector>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
using namespace std;
#define MOD 1000000007
#define INF 1<<30
#define LINF (ll)1<<62
#define rep(i,n) for(ll i=0; i<(n); i++)
#define REP(i,a,b) for(ll i=(a); i<(b); i++)
#define RREP(i,a,b) for(ll i=(a); i>=(b); i--)
#define all(x) (x).begin(),(x).end()
using namespace std;
typedef long long ll;
typedef vector<ll> vl;

int main() {
    ll n; cin >> n;
    vl a;
    for(ll i = 0; i < n; i++) {
        ll num; 
        std::cin >> num;
        a.push_back(num);
    }
    std::multiset<ll> s;
    for(ll i = 0; i < n; i++){
            if (s.empty() || s.upper_bound(-a[i]) == s.end()) {
                 ;
            } else {
                 s.erase(*s.upper_bound(-a[i]));
            }
            s.insert(-a[i]);
    }
    cout << s.size() << endl;
}