For added security, yet another system policy has been put in place. Now, a valid passphrase must contain no two words that are anagrams of each other - that is, a passphrase is invalid if any word's letters can be rearranged to form any other word in the passphrase.

For example:

abcde fghij is a valid passphrase. abcde xyz ecdab is not valid - the letters from the third word can be rearranged to form the first word. a ab abc abd abf abj is a valid passphrase, because all letters need to be used when forming another word. iiii oiii ooii oooi oooo is valid. oiii ioii iioi iiio is not valid - any of these words can be rearranged to form any other word. Under this new system policy, how many passphrases are valid?