866
But first they would need to invent some tape
(i.imgur.com)
They could have fitted the whole ring / tape / mouse assembly into a small paper bag Aragorn could have kept it in his jacket and fed it little bits of lembas on the way how lovely x
Cut to the palace of Mausron the Terrible I: "And that's how we overthrew the apes and founded our perfect paradise, which I now rule with my tiny, iron adorable fist."