Ancient poetry recommendations - preferably not Greek/Roman

I recently finished the Epic of Gilgamesh, and I'm starting a collection of poems by Rumi.

I've previously read Cold Mountain by Han Shan.

Are there any other ancient poets/poems with published work that you'd recommend?

I'm looking for things that are:

• Basically as old as possible
• Poetic/mystic
• Not Christian (or Western, Greek, or Roman).

Thanks!