struct toi_data

		toi_data(const Rcpp::List &impred) : impred(impred) {}

	bool is_immediate_predecessor(int i, int val, const toi_data &d)

		Rcpp::IntegerVector impredi = Rcpp::as<Rcpp::IntegerVector>(d.impred[i-1]);

		return std::find(impredi.begin(), impredi.end(), val) != impredi.end();

	void add_child(int parent, int child, toi_data &d)

		d.children[parent].push_back(child);

	void right(int i, int r, int root, toi_data &d)

		const auto &range = d.children[r];

		std::for_each(range.begin(), range.end(), [=,&d](const int child) {

		  int l = d.label[child];

			if (!is_immediate_predecessor(i, l, d))

				int t = d.parent.size();

				d.parent.push_back(root);

				d.label.push_back(d.label[child]);

				d.children.push_back({});

				add_child(root, t, d);

				right(i, child, t, d);

	int left(int i, toi_data &d)

		int root = d.parent.size();

	  d.label.push_back(i);

	  d.parent.push_back(0);

	  d.children.push_back({});

		if (i == 0)

			return root;

		int r = left(i - 1, d);

		d.parent[r] = root;

		add_child(root, r, d);

		right(i, r, root, d);

		return root;

Rcpp::List treeOfIdeals(Rcpp::List imPred)

	toi_data d(imPred);

	left(imPred.size(), d);

	return Rcpp::List::create(Rcpp::Named("label") = d.label, 

                           Rcpp::Named("parent") = d.parent,

                           Rcpp::Named("child")=d.children);