C++：Abstract class : invalid abstract return type for member function ‘virtual...’

#include <iostream>
#include <cmath>
#include <sstream>
using namespace std;

class aa;
class bb;

class root
{
public:
    virtual ~root() {}
    virtual root add(const aa& a) const=0;
    virtual root add(const bb& a) const=0;
};

class aa: public root
{
public:
    aa() { }
    aa(const aa& a) { }

    virtual root add(const aa& a) const
    { return root(new aa()); }
    virtual root add(const bb& a) const
    { return root(new bb()); }
};

class bb: public root
{
public:
    bb() { }
    bb(const bb& b) {}

    virtual root add(const aa& a) const
    { return root(new bb()); }
    virtual root add(const bb& a) const
    { return root(new bb()); }
};

int main(int argc, char **argv)
{
}

c++ - Abstract class : invalid abstract return type for member function ‘virtual...’ - Stack Overflow