Comparing pairs and sorting them in ascending order

extending sorting to pair<> containers in c++

//This template allows to compare pairs, and return them in ascending order.
template <class T1, class T2, class Pred = std::less<T2> >
struct sort_pair_second {
    bool operator()(const std::pair<T1,T2>&left, const std::pair<T1,T2>&right) {
        Pred p;
        return p(right.second, left.second);
    }
};

//Implementation example
// _noteProducts is an object that contains all the product available.

    for( int i = 0, j = 0; i < _notesProducts.size(); i++){// we assign the name of the products and the number of listed notes.
        
        if ( genderAnswer == _notesProducts[i].gender && _notesProducts[i].listedNotes.size() > 0){// we make sure that we only pass the elements that have the right gender and more than one listed one.

            pair<Products, int> tmp;
            productListedNotes.push_back(tmp);// this is a vector of pairs where we pass the pairs we need only.
            productListedNotes[j] = make_pair (_notesProducts[i], _notesProducts[i].listedNotes.size());
            j++;// we manage our own index for the pair.
        }        
    }
    
// we finally sort from higher to lowest number of listedNotes per fragrance.
    sort(productListedNotes.begin(), productListedNotes.end(), sort_pair_second<Products, int>());// we organize our results based the higher number of notes included in our perfumes