What is the #1 private school in the US?

I'm curious to know, could you elaborate on what criteria are typically used to determine the number one private school in the United States? Is it solely based on academic performance, or do factors such as extracurricular activities, faculty quality, and campus facilities also play a role in the ranking? Additionally, how frequently are these rankings updated, and who conducts the evaluation process? Understanding these details would provide a more comprehensive view of what makes a private school stand out as the best in the country.