Function overload using lambda function signature

Consider the following example

void foo(const std::function<int()>& f) {
    std::cout << f() << std::endl;
}

void foo(const std::function<int(int x)>& f) {
std::cout << f(5) << std::endl;
}

int main() {
    foo([](){return 3;});

    foo([](int x){return x;});
}

This does not compile, because the call to foo is said to be ambiguous. As far as I understand this is due to the fact, that the lambda function is not a priori a std::function but has to be casted to it and that there is a std::function constructor that takes an arbitrary argument.

Maybe someone can explain to me why anyone would create an implicit constructor that takes an arbitrary argument. However my acutual question is whether there is a workaround, which allows to use the function signature of lambda functions to overload a the function foo. I have tried function pointers, but that didn't work because capturing lambda functions can't be cast to a normal function pointer.

Any help is most welcome.