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The most important influences on civilizations in Korea, Japan, and Southeast Asia were China and India.
These two nations spread their culture, systems, traditions, and stories throughout the Japanese, Korean, and Southeast Asia territories through trade and invasions.
One of the most common examples of how this happened was the Silk Road. Yes, the Silkroad, a series of trade routes in the Middle Ages that connected China to Europe, crossing Asia, India, North Africa, the Middle East, and parts of Europe. Particularly, in the case of Japan, the Chinese Tang dynasty heavily influenced art, religion, and the writing system.