How to update/refresh a segment contact count using API?

So we've been trying to automate the process of fetching contacts count in segments via API.

We're able to fetch the count of a segment without any problem using GET.

But the count never gets refreshed unless someone manually goes in the segment and either clicks on the Refresh icon, or Saves the segment to recalculate the count.

I've looked everywhere in the REST API but there's no endpoints allowing us to recalculate the Count of contacts in a segment. I've tried to update on the segment endpoint (using PUT), but all it does is just add the criteria/filters to a segment without recalculating it.