The Hong Kong dollar$($HKD$)$ has long been pegged to the U$.$S$.$ dollar$($USD$)$ at HKD$ $7\mathrm{.}75=$ USD$1\mathrm{.}00.$ When the Chinese yuan$($CNY$)$ was revalued in July $2005$ against the U$.$S$.$ dollar from CNY$8\mathrm{.}28=$ USD$1\mathrm{.}00$ to CNY$8\mathrm{.}11=$ USD$1\mathrm{.}00,$ how did the value of the Hong Kong dollar change against the$$ yuan?