I need some problems that involve Range Minimum/Maximum Query with single element update.

Since I need such problems for some testing and research purposes, it would be good if they are straight forward and don't require anything else other than RMQ (with update queries of course) to solve them. Update queries should be like changing single element. I have already searched on the internet and found many RMQ problems, but none of them involves update queries.

Please provide some links to such problems you know.