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>
typedef long long ll;
#define INF 0x3f3f3f3f
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
using namespace std;
const int sz=1001, mod=1e9+7;

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    int n,i,x;
    cin>>n;
    int a[n];
    for(i=0;i<n;i++)cin>>a[i];
    map<int,int> mp;
    mp[a[0]]++;
    for(i=1;i<n;i++){
        auto it = mp.lower_bound(a[i]);
        if(it==mp.begin()){
            mp[a[i]]++;
        }else{
            --it;
            int x=it->first,y=it->second;
            mp.erase(it);
            if(y!=1) mp[x]=y-1;
            mp[a[i]]++;
        }
    }
    int res=0;
    for(auto x:mp)res+=x.yy;
    cout<<res;
}