In a catchment, there are four rain-gauge stations, $P, Q, R$, and $S$. Normal annual precipitation values at these stations are $780$ mm, $850$ mm, $920$ mm, and $980$ mm, respectively. In the year $2013$, stations $Q, R$, and $S$, were operative but $P$ was not. Using the normal ratio method, the precipitation at station $P$ for the year $2013$ has been estimated as $860\:mm$. If the observed precipitation at stations $Q$ and $R$ for the year $2013$ were $930$ mm and $1010$ mm, respectively; what was the observed precipitation (in mm) at station $S$ for that year?