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>
#define pb push_back
#define mp make_pair
#define se second
#define fi first
#define ll long long int
#define INF INT_MAX
#define mod
#define chutiyaap ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
using namespace std;
ll MinimumNumIncreasingSubsequences(ll arr[], ll n) 
{ 
    multiset<ll> last;
    for (ll i = 0; i < n; i++) {
        multiset<ll>::iterator it = last.lower_bound(arr[i]);
        if (it == last.begin()) 
            last.insert(arr[i]); 
  
        else { 
            it--; 
            last.erase(it); 
            last.insert(arr[i]);  
        } 
    } 
    return last.size();
} 
int main()
{
	chutiyaap;
	ll n;cin>>n;
	ll a[n+1];for(ll i=0;i<n;i++)cin>>a[i];
	cout<<MinimumNumIncreasingSubsequences(a,n);
}