RU-ALLRUSSIAN 1984 Problem 10

$\mathrm{x_1< x_2< x_3< \ldots < x_n}$ . $\mathrm{y_i}$ is a permutation of the $\mathrm{x_i}$ . We have that $\mathrm{x_1 + y_1< x_2 + y_2< \ldots < x_n + }$ $\mathrm{y_n}$ . Prove that $\mathrm{x_i = y_i}$ .