Polynomials with rational values

Here is a cool exercise.
Let P ∈ ℝ[X], deg(P) = n. Suppose that there exist x₀, x₁, …, x_n ∈ ℚ such that P(x_i) ∈ ℚ for all i. Show that P ∈ ℚ[X].

Hint: Vandermonde determinant or Lagrange interpolation