def h_index_brute_force(citation_counts):
    maximum_possible_h_index = len(citation_counts)

    # Iterate downwards from the maximum possible H-index to find the largest valid 'h'
    for candidate_h_index in range(maximum_possible_h_index, -1, -1):
        publications_meeting_criteria = 0

        # Count publications with citations >= the current candidate H-index
        for citation_count in citation_counts:
            if citation_count >= candidate_h_index:
                publications_meeting_criteria += 1

        # Check if the number of qualifying publications meets or exceeds the candidate H-index
        if publications_meeting_criteria >= candidate_h_index:
            return candidate_h_index

    # This case should theoretically not be reached if citation_counts is not empty and contains non-negative values,
    # as h=0 is always a valid H-index (0 publications with >= 0 citations).
    return 0

def calculate_h_index(citation_counts_for_papers):
    sorted_citation_counts = sorted(citation_counts_for_papers, reverse=True)
    number_of_papers = len(sorted_citation_counts)
    potential_h_value = 0

    # Iterate through possible h values, starting from 0.
    for current_h in range(number_of_papers + 1):
        papers_with_enough_citations = 0
        # Count papers that meet or exceed the current potential h value.
        for citation_count in sorted_citation_counts:
            if citation_count >= current_h:
                papers_with_enough_citations += 1
            else:
                # Since the list is sorted, no further papers will meet the criteria.
                break

        # If we have at least 'current_h' papers with 'current_h' or more citations.
        if papers_with_enough_citations >= current_h:
            potential_h_value = current_h
        else:
            # We've found an h value that is too high, so the previous one was the maximum.
            break

    return potential_h_value