input: Write a function to implement a basic machine learning model that performs binary classification on the given data. The model should use the LogisticRegression class from sklearn.linear_model, fit the model to the input data, predict the labels, and calculate the model's accuracy using the accuracy_score function from sklearn.metrics. If the data is empty, return a message indicating that the input data is empty.
  assert binary_classification_model([[0.3, 0.2, 0.6], [0.3, 0.1, 0.4], [0.2, 0.3, 0.4], [0.7, 0.4, 0.2], [0.5, 0.2, 0.1]], [1, 0, 0, 1, 0])=='Model accuracy: 1.0'
  assert binary_classification_model([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]], [1, 0])=='Model accuracy: 0.5'
  assert binary_classification_model([], [])=='The input data is empty.'
output: def binary_classification_model(X, y):
      if not X:
          return 'The input data is empty.'
      from sklearn.linear_model import LogisticRegression
      from sklearn.metrics import accuracy_score
      model = LogisticRegression()
      model.fit(X, y)
      predictions = model.predict(X)
      accuracy = accuracy_score(y, predictions)
      return f'Model accuracy: {accuracy}'