vector<Interval> insert(vector<Interval> &intervals, Interval newInterval) {

   vector<Interval> result;

   bool inserted = false;

   for (auto itv : intervals) {

     if (itv.end < newInterval.start)

       result.push_back(itv);

     else if (itv.start > newInterval.end) {

       if (!inserted) {

         result.push_back(newInterval);

         inserted = true;

       }

       result.push_back(itv);

     }

     else {

       newInterval.start = min(itv.start, newInterval.start);

       newInterval.end = max(itv.end, newInterval.end);

     }

   }

   if (!inserted)

     result.push_back(newInterval);

   return result;

 }