 since his farm is a tree, this means that certain pairs of pastures are connected by corridors so that there is one unique path between any given pair of pastures. FJ believes that some of these paths represent balanced strings of parentheses. In particular, he would like to know, among all such balanced strings represented by paths through the tree, what is the maximum nesting depth one can find. The nesting depth of a balanced string of parentheses is the maximum, over all prefixes of the string, of the 