Let n be a positive integer. Let X be the set of positive integers less than 210n which are multiples of 6, let Y be the set of positive integers less than 210n which are multiples of 10, and let Z be the set of positive integers less than 210n which are multiples of 14. Find the number of permutations of 1,2,3,..,210n in which the elements of X U Y U Z occur in increasing order, but the other numbers in the permutation may occur in any order