Symmetric difference of many sets - c++

Question

The symmetric difference of sets is the set of all elements that do not belong to all the sets. If the sets are already sorted, then I've come up with the solution below that uses std::set_union, std::set_intersection, and std::set_difference. But I'm not convinced that it is the cleanest way to do it. Can someone think of a better (perhaps more efficient) way that uses one simple recursion with variadic template arguments to get the result right away? Perhaps using std::set_symmetric_difference recursively? I have trouble figuring that out. Here is my solution using the above method:
#include <iostream>
#include <vector>
#include <algorithm>
template <typename Container>
std::vector<typename Container::value_type> multi_union (const Container& container) {
return container;
}
template <typename Container1, typename Container2, typename... Containers>
std::vector<typename Container1::value_type> multi_union (const Container1& container1,
const Container2& container2, const Containers&... containers) {
std::vector<typename Container1::value_type> v;
std::set_union (container1.begin(), container1.end(), container2.begin(), container2.end(),
std::back_inserter(v));
return multi_union (v, containers...);
}
template <typename Container>
std::vector<typename Container::value_type> multi_intersection (const Container& container) {
return container;
}
template <typename Container1, typename Container2, typename... Containers>
std::vector<typename Container1::value_type> multi_intersection (const Container1& container1,
const Container2& container2, const Containers&... containers) {
std::vector<typename Container1::value_type> v;
std::set_intersection (container1.begin(), container1.end(), container2.begin(),
container2.end(), std::back_inserter(v));
return multi_intersection (v, containers...);
}
template <typename Container, typename... Containers>
std::vector<typename Container::value_type> multi_symmetric_difference (const Container&
container, const Containers&... containers) {
const std::vector<typename Container::value_type>
a = multi_union (container, containers...),
b = multi_intersection (container, containers...);
std::vector<typename Container::value_type> v;
std::set_difference (a.begin(), a.end(), b.begin(), b.end(), std::back_inserter(v));
return v;
}
int main() {
std::vector<int> a = {3,4,6,1,2}, b = {6,8,9,2}, c = {6,7,4,5,2};
std::sort (a.begin(), a.end()); std::sort (b.begin(), b.end()); std::sort (c.begin(), c.end());
const std::vector<int> s = multi_symmetric_difference (a, b, c);
for (int x : s) std::cout << x << ' '; // 1 3 4 5 7 8 9
}
Also, like std::set_symmetric_difference, multi_symmetric_difference should output to an output iterator so that the resulting container can be of any type (not just vector).