The correct answer to this open question is the following.
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However, we can comment on the following general terms.
The ideas of Confucianism impact the Han Dynasty government and its leaders because Confucious taught and emphasized that rulers should lead by example.
Confucianism was the moral system that strengthens the Han Dynasty. During the Han Dynasty(206BCE-220CE), Confucianism was the dominant ideology.
The teachings of Confucius have come down to our days through his Analects, a collection of aphorisms, maxims, and different anecdotes, probably but not certainly compiled by Confucius' students and is considered a reliable source of Confucius’ view.