5$\cdot$105 In President Milangflos's country, the election for the new president is approaching. There are a total of twenty million voters, but only one percent of the population, the regular army, supports the incumbent president. Milangflos wants to continue being president and also wants the election to be democratic. Therefore, he arranges the "democratic election" as follows: First, all voters are divided into large groups of equal size; each large group is then divided into several sub-groups of equal size; these sub-groups are further divided into smaller groups, and so on, until the smallest groups conduct the first round of elections and elect one representative by simple majority to participate in the next level of elections. Each level of group elections also elects one representative by simple majority, until each large group elects one representative. Finally, these representatives directly elect the president by simple majority. Milangflos can manipulate the grouping and instruct his supporters on how to participate in the election. Can he ensure his re-election through such manipulation?
[Solution] He can win. The president's supporters total 200,000. If the smallest group consists of 5 people and the president arranges his supporters in election groups of 3, then among the 4 million representatives produced after the election, 66,666 support the president. Following this method for 7 levels of elections, the results can be listed as follows:

Then, at the 8th level of elections, each group consists of 8 people, and the president places 5 of his supporters in each group. Thus, among the 32 representatives produced, 18 are supporters of the president. This time, the president can be directly elected.