Let S be a set of positive integers satisfying the following two conditions:
(i) for each positive integer n, at least one of n,2n,…,100n is in S;
(ii) if a1,a2,b1,b2 are positive integers such that gcd(a1a2,b1b2)=1 and a1b1,a2b2∈S, then a2b1,a1b2∈S.
Suppose that S has natural density r, meaning limn→∞n1∣S∩{1,…,n}∣=r. Compute the minimum possible value of ⌊105r⌋.