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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<unordered_map>

using namespace std;
typedef pair<long long int, long long int> P;

long long int INF = 1e18;
long long int MOD = 1e9 + 7;

long long int memo[210000], A[210000];

int main(){
  int N;
  cin >> N;
  for(int i = 0; i <= N; i++){
    memo[i] = INF;
  }
  for(int i = 0; i < N; i++){
    cin >> A[i];
  }
  reverse(A, A + N);
  for(int i = 0; i < N; i++){
    int pos = distance(memo, upper_bound(memo, memo + N, A[i]));
    memo[pos] = A[i];
  }
  cout << distance(memo, lower_bound(memo, memo + N, INF)) << endl;
  return 0;
}