class Queue:
    __slots__ = ('_events', '_amounts')

    def __init__(self, events=None):
        if events is None:
            events = []
        self._events = events
        self._amounts = {}
        if isinstance(events, list):
            for event in events:
                if isinstance(event, dict) and 'id' in event and 'cents' in event:
                    request_id = event['id']
                    cents = event['cents']
                    if isinstance(cents, int) and not isinstance(cents, bool) and request_id not in self._amounts:
                        self._amounts[request_id] = cents

    @property
    def events(self):
        return self._events

    def enqueue(self, request_id, cents):
        if isinstance(cents, bool) or not isinstance(cents, int):
            raise TypeError('cents must be an integer')
        if cents <= 0:
            raise ValueError('cents must be positive')
        if request_id in self._amounts:
            existing = self._amounts[request_id]
            if existing == cents:
                return 'duplicate'
            raise ValueError('request id already used with a different amount')
        event = {'id': request_id, 'cents': cents}
        self._events.append(event)
        self._amounts[request_id] = cents
        return 'queued'