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This is actually a very insightful question.

First, you have to understand the concept of distance in the pre-modern world.

Both Japan and Korea were far closer to China than places like

Sichuan and Tibet because the former 2 are accessible by sea. This allowed direct transfer of Chinese culture from the heart of China on the Yellow and Yangtze deltas to Korea and Japan whereas Tibet and Mongolia were relatively neglected by Chinese travelers and merchants.

Simply put, overland travel was a bummer back in those days, whereas sea travel was a breeze.

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