Fisher Information, on discrete uniform distribution

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suppose that I have a sample with n observations $X_1,X_2...X_n$ that each follows discrete uniform distribution $DU(1,\theta)$, where the smallest possible value is 1, and the largest is n. So the probability function is $1/\theta$.

And my question is, what is the fisher information for parameter "$\theta$".

And what is Jeffreys prior for it?

Thanks