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;
int n;
multiset<int>s;
multiset<int>::iterator it;
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        int x;
        scanf("%d",&x);
        if(s.empty()) s.insert(x);
        else
        {
            it=s.lower_bound(x);
            if(it==s.begin()) s.insert(x);
            else
            {
                it--;
                s.erase(s.find(*it));
                s.insert(x);
            }
        }
    }
    printf("%d\n",s.size());
}