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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

bool comp(int a, int b)
{
	return a > b;
}

int main()
{
	int n;
	cin >> n;
	vector<int> a(n + 1, -1);
	for (int i = 0; i < n; i++) {
		int b;
		cin >> b;
		int t = upper_bound(a.begin(), a.end(), b, comp) - a.begin();
		a[t] = b;
	}

	for (int i = 1; i <= n; i++) {
		if (a[i] == -1) {
			cout << i << endl;
			return 0;
		}
	}

	return 0;
}