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public class Test {

    private static Map<Integer, Integer> result = new HashMap<>();

    private static ArrayList<Integer> remaining(final ArrayList<Integer> input, final int digit) {
        ArrayList<Integer> remaining = new ArrayList<>(input);
        remaining.remove(input.indexOf(digit));
        return remaining;
    }

    private static Stack<Integer> getCandidates(final ArrayList<Integer> input, final int lower, final int higher) {
        List<Integer> filtered = input.stream()
                .filter(num -> num >= lower && num <= higher)
                .sorted()
                .collect(Collectors.toList());
        Stack<Integer> result = new Stack<>();
        result.addAll(filtered);
        return result;
    }

    public static int findFirst(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 2);
        for (Integer candidate : candidates) {
            final int next = findSecond(remaining(input, candidate));
            if (next != -1) {
                result.put(0, candidate);
                return candidate;
            }
        }
        return -1;
    }

    public static int findSecond(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 9);
        for (Integer candidate : candidates) {
            final int next = findThird(remaining(input, candidate));
            if (next != -1) {
                result.put(1, candidate);
                return candidate;
            }
        }
        return -1;
    }

    public static int findThird(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 5);
        for (Integer candidate : candidates) {
            final int next = findFourth(remaining(input, candidate));
            if (next != -1) {
                result.put(2, candidate);
                return candidate;
            }
        }
        return -1;
    }

    public static int findFourth(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 9);
        for (Integer candidate : candidates) {
            final int next = findFifth(remaining(input, candidate));
            if (next != -1) {
                result.put(3, candidate);
                return candidate;
            }
        }
        return -1;
    }

    public static int findFifth(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 5);
        for (Integer candidate : candidates) {
            final int next = findLast(remaining(input, candidate));
            if (next != -1) {
                result.put(4, candidate);
                return candidate;
            }
        }
        return -1;
    }

    public static int findLast(final ArrayList<Integer> input) {
        Stack<Integer> candidates = getCandidates(input, 0, 9);
        if (candidates.isEmpty()) {
            return -1;
        }

        Integer last = candidates.peek();
        result.put(5, last);
        return last;
    }

    public static void main(String[] args) {
        final ArrayList<Integer> input = new ArrayList<>(Arrays.asList(1, 2, 3, 4, 6, 8));

        findFirst(input);
        System.out.println(result.values());
    }
}