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Implementation of dynamic ranking for a colummn in an individual table

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I have various tables in which each record has an associate rank. The rank given is not an automatic, calculated rank but a manual rank decided by me.

I want the rank to be dynamic so that if I add a new row which should be ranked somewhere in the middle of the total order then all other entries in the same table have their rank change accordingly.

I do not need the rank to taken into account any other tables, the rank is specific to each table individually.

Is this possible?

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