#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>

using namespace std;

vector<int> find_lis(vector<int> A)
{
  vector<int> m;
  vector<int> p(A.size());

  int i, begin, end, mid;

  m.push_back(0);

  for (i = 1; i < A.size(); i++){
    if (A[m.back()] <= A[i]){
      p[i] = m.back();   // the order here is important
      m.push_back(i);
      continue;
    }

    for (begin = 0, end = m.size() -1; begin < end; ){
      mid = (begin + end) / 2;
      if (A[m[mid]] <= A[i]) 
        begin = mid + 1;
      else
        end = mid;
    }

    if (A[i] < A[m[begin]]){
      m[begin] = i;
      if (begin > 0) p[i] = m[begin - 1]; 
    }
  }

  vector<int> result;
  int pos ;

  pos = m.back(); 
  for (i = m.size(); i > 0; i--){
    result.push_back(A[pos]);
    pos =  p[pos];
  }

  reverse(result.begin(), result.end());
  return result; 
}

int main()
{
  int a[] = { 7, 8, 9, 10, 1, 2, 3, 3, 3, 4, 6, 7, 5, 8}; //14

  vector<int> A(a, a + sizeof(a) / sizeof(int));
  ostream_iterator<int> oit(cout, " ");

  vector<int> lis = find_lis(A);

  copy(A.begin(), A.end(), oit);
  cout << endl;

  copy(lis.begin(), lis.end(), oit);
  cout << endl;

  return 0;
}