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;
using ll = long long;

ll solve() {
    ll N;
    cin >> N;
    map<ll, int> num;
    ll a;
    for ( int i = 0; i < N; i++ ) {
        cin >> a;
        a = -a;
        auto x = num.upper_bound(a);
        if ( x == num.end() ) {
            num[a]++;
        } else {
            num[a]++;
            num[x->first]--;
            if ( num[x->first] == 0 ) {
                num.erase(x->first);
            }
        }
    }
    ll s = 0;
    for( auto x : num ) {
        s += x.second;
    }
    return s;
}

int main() {
    auto ans = solve();
    cout << ans << "\n";
    return 0;
}