List has custom object with overlap date ranges need to break all overlap ranges into new periods and keep non overlap AS IS in java

Question

Consider below example , inputList has overlap date ranges

        inputList.add(new DateRange(LocalDate.of(2023, 7, 1), LocalDate.of(2023, 7, 10)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 5), LocalDate.of(2023, 7, 30)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 10), LocalDate.of(2023, 7, 20)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 15), LocalDate.of(2023, 7, 20)));
        inputList.add(new DateRange(LocalDate.of(2023, 8, 1), LocalDate.of(2023, 8, 20)));

Need to merge all overlap period and keep remaining non overlap period in resultList

        resultList(new DateRange(LocalDate.of(2023, 7, 1), LocalDate.of(2023, 7, 04)));
         resultLis(new DateRange(LocalDate.of(2023, 7, 5), LocalDate.of(2023, 7, 09)));
         resultLis(new DateRange(LocalDate.of(2023, 7, 10), LocalDate.of(2023, 7, 10)));
         resultLis(new DateRange(LocalDate.of(2023, 7, 11), LocalDate.of(2023, 7, 14)));
         resultLis(new DateRange(LocalDate.of(2023, 7, 15), LocalDate.of(2023, 7, 20)));
         resultLis(new DateRange(LocalDate.of(2023, 7, 21), LocalDate.of(2023, 7, 30)));
         resultLis(new DateRange(LocalDate.of(2023, 8, 1), LocalDate.of(2023, 8, 20)));

With below code after overlap periods not splitting

class DateRange {
    LocalDate start;
    LocalDate end;

    public DateRange(LocalDate start, LocalDate end) {
        this.start = start;
        this.end = end;
    }

    @Override
    public String toString() {
        return "DateRange [start=" + start + ", end=" + end + "]";
    }
}

public class Main1 {
    public static void main(String[] args) {
        List<DateRange> inputList = new ArrayList<>();
        inputList.add(new DateRange(LocalDate.of(2023, 7, 1), LocalDate.of(2023, 7, 10)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 5), LocalDate.of(2023, 7, 30)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 10), LocalDate.of(2023, 7, 20)));
        inputList.add(new DateRange(LocalDate.of(2023, 7, 15), LocalDate.of(2023, 7, 20)));
        inputList.add(new DateRange(LocalDate.of(2023, 8, 1), LocalDate.of(2023, 8, 20)));

        List<DateRange> resultList = processDateRanges(inputList);
        resultList.forEach(System.out::println);
    }
    public static List<DateRange> processDateRanges(List<DateRange> inputList) {
        List<DateRange> result = new ArrayList<>();
        Collections.sort(inputList, Comparator.comparing(r -> r.start));

        for (int i = 0; i < inputList.size(); i++) {
            DateRange current = inputList.get(i);
            LocalDate start = current.start;
            LocalDate end = current.end;

            for (int j = i + 1; j < inputList.size(); j++) {
                DateRange next = inputList.get(j);
                if (next.start.isAfter(end.plusDays(1))) break;

                if (next.start.isAfter(start)) {
                    result.add(new DateRange(start, next.start.minusDays(1)));
                }
                if (next.end.isBefore(end)) {
                    result.add(new DateRange(next.start, next.end));
                    start = next.end.plusDays(1);
                } else {
                    start = next.start;
                    end = next.end;
                }
            }
            result.add(new DateRange(start, end));
            while (i + 1 < inputList.size() && inputList.get(i + 1).start.isBefore(end.plusDays(1))) {
                i++;
            }
        }

        return result;
    }

}

Getting output as

1. 2023-07-01 - 2023-07-04
2. 2023-07-05 - 2023-07-09
3. 2023-07-10 - 2023-07-20
4. 2023-07-15 - 2023-07-20
5. 2023-07-21 - 2023-07-30
6. 2023-08-01 - 2023-08-20

Expecting as below

1. 2023-07-01 - 2023-07-04 - Before overlap period of 1st record
2. 2023-07-05 - 2023-07-09 - overlap with 1st and 2nd record
3. 2023-07-10 - 2023-07-10 - overlap with 1st, 2nd and 3rd record
4. 2023-07-11 - 2023-07-14 - overlap with 2nd and 3rd record
5. 2023-07-15 - 2023-07-20 - overlap with 2nd , 3rd and 4th record
6. 2023-07-21 - 2023-07-30 - after overlap period of 2nd record
7. 2023-08-01 - 2023-08-20 - Non overlap period