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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int a[100001],d[100001],n;
int main() {
	cin>>n;
	for(int i=1; i<=n; i++)cin>>a[i];
	int l=1;
	d[1]=a[1];
	for(int i=2; i<=n; i++) {
		if(d[l]>=a[i])d[++l]=a[i];
		else {
			int p=upper_bound(d+1,d+1+l,a[i],greater<int>())-d;
			d[p]=a[i];
		}
	}
	cout<<l;
	return 0; 
}