def solution(members, events):
    # Initialize a dictionary to keep track of mentions count for each member
    mention_count = {member: 0 for member in members}

    # Initialize a dictionary to keep track of active status and offline expiry times
    active_status = {member: True for member in members}
    offline_expiry = {member: 0 for member in members}

    for event in events:
        event_type = event[0]
        timestamp = int(event[1])

        # Update the active status of users based on the current timestamp
        for member in members:
            if offline_expiry[member] <= timestamp:
                active_status[member] = True

        if event_type == "MESSAGE":
            mentions = set(event[2].split())
            all_mentioned = set()

            # Process "ALL" mention
            if "ALL" in mentions:
                all_mentioned.update(members)
                mentions.remove("ALL")

            # Process "HERE" mention
            if "HERE" in mentions:
                for member in members:
                    if active_status[member]:
                        all_mentioned.add(member)
                mentions.remove("HERE")

            # Add specific mentions
            for mention in mentions:
                if mention in members:
                    all_mentioned.add(mention)

            # Count mentions for valid members (ignore duplicate mentions in a single event)
            valid_mentions = set()
            for member in all_mentioned:
                valid_mentions.add(member)

            # Update the mention counts
            for member in valid_mentions:
                mention_count[member] += 1

        elif event_type == "OFFLINE":
            user_id = event[2]
            if user_id in members:
                active_status[user_id] = False
                offline_expiry[user_id] = timestamp + 60

    # Generate the result list
    result = [f"{member}={mention_count[member]}" for member in sorted(members)]

    return result

# Test the function
members = ["id42", "id158", "id23"]
events = [
    ["MESSAGE", "0", "ALL id158 id42"],
    ["OFFLINE", "1", "id158"],
    ["MESSAGE", "2", "id158 id158"],
    ["OFFLINE", "3", "id23"],
    ["MESSAGE", "60", "HERE id158 id42 id23"],
    ["MESSAGE", "61", "HERE"]
]
print(solution(members, events))  # Output should be ["id158=4", "id23=2", "id42=3"]