Math Problem Solver

Five people are in a group, including Kai and Wen. To practice social distancing, they first take the step of splitting the group into two disjoint subgroups. Then, they undergo a series of additional steps, during each of which they divide every remaining subgroup that has more than 1 person into two further subgroups. The steps end when every person is alone. Due to a long-standing grudge, Kai and Wen cannot be together in the same subgroup after the first division. Considering that the order of divisions matters and all remaining subgroups are divided simultaneously at each step, how many possible division pathways exist? A division pathway is considered the full process starting from 1 group of 5 and ending at 5 groups of 1. Please enter ONLY the number.