Web of Conspiracies

You may cast Web of Conspiracies as though it has flash as long as X target players control no nonland permanents.
Choose a card type. Up to X target players search their libraries for a card with that card type, reveals it to each player who searched their library this way, then puts it into his or her hand. Each player who searched their library for a card this way shuffles it afterwards. X can't be 1.