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;

const int MAXN = 2e5;

int n, a[MAXN], ans;
multiset<int> leaf;

int main(){
	scanf("%d", &n);
	for(int i = 0; i < n; ++i){
		scanf("%d", &a[i]);
	}
	for(int i = 0; i < n; ++i){
		if(leaf.empty()){
			ans++;
		}else{
			auto p = leaf.lower_bound(a[i]);
			if(p == leaf.begin()){
				ans++;
			}else{
				p--;
				leaf.erase(p);
			}
		}
		leaf.insert(a[i]);
	}
	printf("%d\n", ans);
}