Xeniathe mathematician has a sequence consisting ofn(nis divisible by 3) positive integers, each of them is at most 7. She wants to split the sequence into groups of three so that for each group of threea,b,cthe following conditions held:
·a<b<c;
·adividesb,bdividesc.
Naturally, Xenia wants each element of the sequence to belong to exactly one group of three. Thus, if the required partition exists, then it hasgroups of three.
Help Xenia, find the required partition or else say that it doesn't exist.