CN-TST 2023 Problem 2

$n$ people attend a party. There are no more than $n$ pairs of friends among them. Two people shake hands if and only if they have at least $1$ common friend. Given integer $m\ge 3$ such that $n\leq m^3$ . Prove that there exists a person $A$ , the number of people that shake hands with $A$ is no more than $m-1$ times of the number of $A$ 'S friends.