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 <bits/stdc++.h>
using namespace std;

#define mp make_pair
typedef long long ll;
typedef pair<int,int>pii;
const int N = 1e5;
int arr[N+100];
multiset<int>st;

int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&arr[i]);
	}
	for(int i=1;i<=n;i++){
		auto it = st.lower_bound(arr[i]);
		if(it==st.begin())st.insert(arr[i]);
		else{
			it--;
			st.erase(*it);
			st.insert(arr[i]);
		}
	}
	printf("%d\n",(int)st.size());
}