input: def classify_string(input_string: str) -> str:
      """
      Classify a given input string using a pre-trained machine learning classifier. 
      The classifier is trained using a Multinomial Naive Bayes model.
      
      >>> classify_string("This is a test input")
      'class_1'
      >>> classify_string("Another example of input")
      'class_2'
      """
output:     from sklearn.feature_extraction.text import CountVectorizer
      from sklearn.naive_bayes import MultinomialNB
  
      # Pre-trained model and vectorizer
      vectorizer = CountVectorizer()
      classifier = MultinomialNB()
  
      # Example training data
      train_data = ["This is a test input", "Another example of input"]
      train_labels = ["class_1", "class_2"]
  
      # Fit the model
      X_train = vectorizer.fit_transform(train_data)
      classifier.fit(X_train, train_labels)
  
      # Transform the input string
      X_input = vectorizer.transform([input_string])
  
      # Predict the class
      predicted_class = classifier.predict(X_input)
  
      return predicted_class[0]