JavaEE CDI initialize subclasses after @PostConstruct

I want to initialize subclasses after a @PostConstruct of the super class

So I do somthing like that

// case 1: it's working but it's not simple to understand

public class A {

    @PostConstruct
    protected void init() {
        System.out.println("A");
        afterInit();
    }

    protected void afterInit() {}

}

public class B extends A {

    @Override
    protected void afterInit() {
        System.out.println("B");
    }

}


public class C extends B {

    @Override
    protected void afterInit() {
        super.afterInit();
        System.out.println("C");
    }

}

So the init() method will print A, B, C in this order

It would be fine to have a @AfterPostconstruct annotation that would do the same but I don't find out

// case 2: dream code

public class A {

    @PostConstruct
    protected void init() {
        System.out.println("A");
    }

}

public class B extends A {

    @AfterPostConstruct  // pseudocode
    protected void afterInitB() {
        System.out.println("B");
    }

}


public class C extends B {

    @AfterPostConstruct // pseudocode
    protected void afterInitC() {
        System.out.println("C");
    }

}

I try by overriding init() but it doesn't work (init() is not called by the container)

// case 3 : code that is not working but it would be better than case 1

public class A {

    @PostConstruct
    protected void init() {
        System.out.println("A");
    }

}

public class B extends A {

    @Override
    protected void init() {
        super.init();
        System.out.println("B");
    }

}


public class C extends B {

    @Override
    protected void init() {
        super.init();
        System.out.println("C");
    }

} 

is there a better (simplier) way to initialize subclasses after @PostConstruct ?