Let's discuss a problem, new variant of Rotate Array

I thought a variant of Rotate Array. Assume that there are the same items in the array. What we want to get is not the minimum item. We want to get the index of the first minimum item before rotating. For example, 1,1,1,1,2,1,1,1, we don't want the first '1' (which got by general method). We want to get the index of '1' after '2'. How to solve this problem by Binary Search? Thanks in advance.

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