At the end of June, we'll be flying into Bozeman and staying in Livingston our first night in Montana. The next morning we plan on getting an early start and heading down to Yellowstone and exploring the north part of the park. We then plan to take the Beartooth Passway to Red Lodge where we'll have dinner and stay overnight. Is this doable? When do we need to leave the park to make it to Red Lodge comfortably before it gets dark?