$A,B,C$ are three piles of rocks. The mean weight of the rocks in $A$ is $30$ pounds, the mean weight of the rocks in $B$ is $60$ pounds, the mean weight of the rocks in the combined piles $A$ and $B$ is $36$ pounds, and the mean weight of the rocks in the combined piles $A$ and $C$ is $38$ pounds. What is the greatest possible integer value for the mean in pounds of the rocks in the combined piles $B$ and $C$?