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;
template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }
#define pb push_back
#define mp make_pair
#define cotu cout
#define itn int
#define Red ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define F first
#define S second
#define sz(x) (int)x.size()
#define all(x) (x).begin(), (x).end()
#define rep(i, n) for(int i = 0; i < n; ++i)
#define repr(i,n) for(int i = n - 1; i >= 0; --i)
#define Rep(i, a, n) for(int i = (a); i <=(n); ++i)
#define repst(i, n) for(auto it = n.begin(); it != n.end(); ++it)
#define Repr(i, a, n) for(int i = (n); i >= (a); --i)
typedef long long ll;
 
const int inf = int(1e9);
const int mod = inf + 7;
const int N = 1e6 + 555;
const double PI = acos(-1.0);

void solve()
{
	int n;
	cin >> n;
	itn a[n];
	multiset<int> st;	
	rep(i, n) {
		cin >> a[i];
	}
	int cnt = 0;
	for(int i = 0; i < n; ++i){
		auto it = st.lower_bound(a[i]);
		if(it == st.begin()) st.insert(a[i]);
		else{
			it--;
			st.erase(it);
			st.insert(a[i]);
		}
	}
	cout << sz(st);

}	
int main()
{
	Red;
	solve();
	return 0;
}