Write down a chain of integers between 1 and 100, with no repetition, such that if x and y are consecutive numbers in the chain, then x evenly divides y or y evenly divides x. Here is an example of such a chain, with length 12:

37, 74, 2, 8, 4, 16, 48, 6, 3, 9, 27, 81

What is the longest chain you can find?