template<size_t dim>
double pathLength2(points<dim> ps){
    if(ps.size() < 2){
        return 0;
    }
    point<dim> prev = ps[ps.size()-1];
    return accumulate(ps.begin(), ps.end(), 0.0, [&prev](double acc, point<dim> &p)->double{
            double ret = acc + dist(prev, p);
            prev = p;
            return ret;
            });
}