Learning about trees

A program takes as input a balanced binary search tree with $n$ leaf nodes and computes the value of a function $g(x)$ for each node $x$ . If the cost of computing $g(x)$ is the minimum value between the {number of leaf-nodes in left-subtree of $x$ , and the number of leaf-nodes in $x$ , then the worst-case time complexity of the program is $\text{\_\_\_\_\_\_\_\_\_\_\_\_\_}$ .