Why $\lambda_i(X + Y) \leq \min \left\{ \lambda_j(X) + \lambda_k(Y): j + k = i + n \right\}$? for Hermitian matrices with ordered eigenvalues

Question

Please explain why $$\lambda_i(X + Y) \leq \min \left\{ \lambda_j(X) + \lambda_k(Y): j + k = i + n \right\}, $$ if $X \in M_n$ and $Y \in M_n$ are Hermitian and their eigenvalues are arranged in non-decreasing order.

Thank you so much in advance