Triglav National Park - Hike recommendations

Hello everybody! A friend and I are currently planning our trip to Slovenia in a few months. We also want to spend a few days in and around Triglav National Park to hike and spend time in nature. We will be in Triglav National Park at the very beginning of June and are looking for a multi-day route with 1-2 overnight stays in huts. I have already read that some huts only open in mid-June and that not all trails can be hiked yet (depending on the year, of course). We are sporty types with average hiking experience. Do you have any recommendations for a loop tour with 1-2 overnight stays in huts for that time of the year? Do you have any other tips on what we should bear in mind?

Thanks in advance! We're really looking forward to visiting your country