Again, using only Max Path as our difficulty gauge, ideal convergent brackets containing 8 or even 16 segments could qualify as "Medium" (see hypothetical bracket scores in Figure ). Intuitively this classification would not make sense, as the current record among published brackets is 10 segments. However, it is evident from this analysis that as more segments are introduced, the possibility of an ideal ligation strategy diminishes rapidly, and thus large brackets with low Max Path are extremely rare.