#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <string>

using namespace std;

#define BE(v) (v).begin(), (v).end()
#define INS(v) inserter (v, v.end ())

template < class T > ostream &	// template to print any vector 
  operator << (ostream & os, vector < T > v)
{
  for (int i = 0; i < v.size (); i++)
    os << " " << v[i];
  os << "\n";
  return os;
}


template < class iter > void
view (ostream & os, iter b, iter e)
{
  iter it;
  for (it = b; it != e; it++) {
    os << *it << " ";
  }
  os << "\n";
}


template < class T > 
void
insertsorted (vector < T > &vec, T val)
{
typedef typename vector<T>::iterator Titer;
pair<Titer,Titer> iter;
  iter = equal_range (BE (vec), val);
  if (iter.first==iter.second) {
    vec.insert (iter.first, val);
  }
}


template < class T > 
void
insertsorted (vector <T> & vec, const vector <T> & vals) {
for (int i=0; i < vals.size(); i++)
  insertsorted(vec,vals[i]);
}


template < class T > void
erasesorted (vector < T > &vec, T val)
{
  if (vec.size()) {
  typename vector < T >::iterator it;
  it = lower_bound (BE (vec), val);
  if (it == vec.end())
    return;
  if (*it == val) {
    vec.erase (it);
  }
  }
}

template < class T > void
erasesorted (vector <T> & vec, const vector <T> & vals) {
for (int i=0; i < vals.size(); i++)
  erasesorted(vec,vals[i]);
}

template < class T > string
all2string (T in, int i)
{
  stringstream s;
  s << in;
  string ss;
  ss = s.str ();
  while (ss.length () < i)
    ss = "0" + ss;
  return ss;
}