Quasi-Markov-chain version:
https://tio.run/##fVJNb9swDL3rVxDexcG6osNuw3rI1q3AvlAsKHooioCRaYuoLBkyvcT985loO8Paw25P71GPj5S6UVwM745HbruYBBKGKrbG/Fz/@LyBS7gvqMWQqB9gXZxBcZuxR6EKNpI4NMpZ5FSBjRwcKYfoFsWNHaU3gQatjcpcfY@9VeDHA3oF3YEaSoruHKHAHT9hqvT8cdjt/Cz9wur36Gu4SbFJ2PbKXecms3ozNthSupjYhBzg2sVe9LgRqmsME6SmmVEbh54Eeer/NcK3Je6aKwrwycX9VIXiLE4uV4z@S1osZdxFG7s82SOJeJrzPZFwS8WDMRXV0OIjbUMOVa7eG9D1ecnbLAoDymY4L/rcusiWymndKwOclQsDe8ee8uEDeAql3lAbsENKFGTrc19KuVSVe37I0tLi9eWLoiy9gs2exTqQCAiB9nMEPD02cA0s@f1CXknoQRxBrxV/HfKd7X9jq8WLcPkRTtc0@mnsE6cULxOcc6joUD43mFx1nre6PxlSWGY0psufScp/Vrw6Hv8A