CN-TST 2022 Problem 12

Let $m,n$ be two positive integers with $m \ge n \ge 2022$ . Let $a_1,a_2,\ldots,a_n,b_1,b_2,\ldots,b_n$ be $2n$ real numbers. Prove that the numbers of ordered pairs $(i,j) ~(1 \le i,j \le n)$ such that $$|a_i+b_j-ij| \le m$$ does not exceed $3n\sqrt{m \log n}$ .