Walks, Paths and Connectivity · Hard problem

A graph consists of a $7$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}7\text{-}1$ together with one additional chord $14$ (edges $12,23,34,45,56,67,71,14$). How many distinct cycles does this graph contain in total?