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: Time Limit Exceeded)

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using Vi = vector<int>;
using Vl = vector<ll>;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

//===



int main() {
	int N;
	cin >> N;
	Vi a(N);
	for (int i = 0; i < N; ++i) {
		cin >> a[i];
	}

	int ans = 1;
	Vi color_min;
	color_min.push_back(a[N - 1]);
	for (int i = N - 2; i >= 0; --i) {
		int j;
		for (j = 0; j < ans; ++j) {
			if (a[i] < color_min[j]) {
				color_min[j] = a[i];
				break;
			}
		}
		if (j == ans) {
			++ans;
			color_min.push_back(a[i]);
		}
	}

	cout << ans << endl;
}