A nice number is a natural number such that its square and cube combined contain all digits exactly once, without needing to use any leading zeros. A semi-nice number is a number that is not nice in a given base, but would be nice in that base if leading zeros were allowed. Currently, the only known semi-nice number is 5: In base six, 5^2 = 41 and 5^3 = 325, covering all the digits except zero.

This market resolves YES if it is proven that 5 is the only semi-nice number in any base, and NO if it is proven that another semi-nice number exists.

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