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;
typedef long long ll;
#define rep(i,n) for(int i=0;i<(n);i++)

int main(int argc, char const *argv[])
{
	int n; cin >> n;
	vector<int> a(n); rep(i, n) cin >> a[i];
	set<int> st; rep(i, n) st.insert(i);

	int ans = 0;
	while(not st.empty()) {
		ans++;
		vector<int> erase;
		int now = -1;
		for (auto u : st) {
			if (now < a[u]) {
				now = a[u];
				erase.push_back(u);
			}
		}
		for (auto u : erase) st.erase(u);
	}
	cout << ans << endl;

	return 0;
}