Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in C++ (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
using namespace std;

int main(){

  int n;
  int dp[100001] = {};
  int a[100001] = {};

  cin >> n;
  for(int i = 0; i < n; i++){
    cin >> a[i];
  }
  int len = 1;
  dp[0] = a[0];
  for(int i = 1; i < n; i++){
    if(dp[len-1] < a[i]){
      dp[len++] = a[i];
    }else{
      *lower_bound(dp, dp+len, a[i]) = a[i];
    }
  }
  cout << len << endl;
  return 0;
}