Prove that the coefficient of $x^n$ in the polynomial $p(x)=\sum_{i=0}^{n}y_iℓ_i(x)$ is $\sum_{i=0}^{n}y_i\prod_{j=0, i\neq j}^{n}(x_i-x_j)^{-1}$

Question

Prove that the coefficient of $x^n$ in the polynomial $p(x)=\sum_{i=0}^{n}y_iℓ_i(x)$ is $\sum_{i=0}^{n}y_i\prod_{j=0, i\neq j}^{n}(x_i-x_j)^{-1}$

I know that $ℓ_i(x)=\prod_{j=0, i\neq j}^{n}\frac{x-x_j}{x_i-x_j}$ where P are obtained from the Lagrange interpolation, then this is reduced to finding the $x^n$ coefficient of $\sum_{i=0}^{n}y_i\prod_{j=0, i\neq j}^{n}\frac{x-x_j}{x_i-x_j}$, how can you do this easily?