Consider the following statements with reference to the differences between Hindustani and Carnatic classical music:
1. Hindustani music synthesized with Vedic, Islamic and Persian traditions, while Carnatic is developed without external influences.
2. Hindustani music has various gharanas like Lucknow, Jaipur, Kirana, Agra, etc., wherein Carnatic music no such gharanas are found.
Which of the statements given above is/are correct?