//  find  maximum  in  vector
 int  find_max(const  std::vector<int>  &v)  {
     int  max  =  0;
     for  (int  i  =  0  ;  i  <  v.size()  ;  ++i)
             if  (max  <  v[i])
                     max  =  v[i];
     return  max;
 }