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 <set>

using namespace std;
int n,a[100010];
bool solve(int k){
	multiset<int> m;
	for(int i=0;i<n;i++){
		if(m.size()<k) m.insert(a[i]);
		else{
			int x = *m.begin();
			if(x>=a[i]) return false;
			auto it = m.lower_bound(a[i]);
			it--;
			m.erase(it); m.insert(a[i]);
		}
	}
	return true;
}
			
int main(){
	int i;
	cin >> n;
	for(i=0;i<n;i++){
		cin >> a[i];
	}
	int l = 0,r = n;
	while(r - l>1){
		int mid = (l + r)/2;
		if(solve(mid)) r = mid;
		else l = mid;
	}
	cout << r << endl;
}