RMO 2019 Problem 6

Suppose $91$ distinct positive integers greater than $1$ are given such that there are at least $456$ pairs among them which are relatively prime. Show that one can find four integers $a, b, c, d$ among them such that $\gcd(a,b)=\gcd(b,c)=\gcd(c,d)=\gcd(d,a)=1.$