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: Time Limit Exceeded)

#include <iostream>
#include <vector>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> v(n), d(n);
  for(int i=0;i<n;i++) cin >> v[i];

  for(int i=0;i<n;i++)
    for(int j=i+1;j<n;j++)
      if(v[j]>v[i])
        d[j] = max(d[j], d[i]+1);

  int ans = 0;
  for(int i=0;i<n;i++)
    ans = max(ans, d[i]);
  cout << ans + 1<< endl;
  return 0;
}