input: def sentiment_analysis(tweets):
      """
      Perform sentiment analysis on a list of tweets and classify each tweet as either
      'Positive' or 'Negative'. The tweets are first preprocessed and then vectorized.
      The vectorized tweets are predicted using a sentiment prediction model.
  
      >>> sentiment_analysis(['I love this product!', 'I hate this product.'])
      ['Positive', 'Negative']
      >>> sentiment_analysis(['This is amazing!', 'Not happy with this at all.'])
      ['Positive', 'Negative']
      """
      # Initialize a list to store the result 
      results = [] 
  
      # Iterate through each tweet
      for tweet in tweets:
          # Clean the tweet 
          tweet = preprocessing(tweet)
  
          # Vectorize the tweet and obtain the prediction 
          tweet_vector = vectorize(tweet)
          prediction = predict_sentiment(tweet_vector)
  
          # Append the prediction to the result list
          if prediction == 1:
              results.append("Positive")
          elif prediction == 0:
              results.append("Negative")
  
      return results
output:     # Define the preprocessing function
      def preprocessing(tweet):
          # Example: Remove punctuation and convert to lowercase
          import string
          tweet = tweet.translate(str.maketrans('', '', string.punctuation))
          tweet = tweet.lower()
          return tweet
  
      # Define the vectorize function
      def vectorize(tweet):
          # Example: Use a simple bag of words approach
          from sklearn.feature_extraction.text import CountVectorizer
          vectorizer = CountVectorizer()
          vectorizer.fit([tweet])
          return vectorizer.transform([tweet]).toarray()[0]
  
      # Define the predict_sentiment function
      def predict_sentiment(tweet_vector):
          # Example: Use a simple rule-based model
          if tweet_vector.sum() > 0:
              return 1  # Positive
          else:
              return 0  # Negative