class Queue:
    def __init__(self,events=None):
        self.events=[] if events is None else events
        self.seen={}
    def enqueue(self,key,cents):
        if type(cents) is not int or cents<=0:raise ValueError('amount')
        if key in self.seen:
            if self.seen[key]!=cents:return 'duplicate'
            return 'duplicate'
        self.events.append({'id':key,'cents':cents})
        self.seen[key]=cents
        return 'queued'