Before revision:  At the heart of our algorithm are a combination of two kinds of tree-decompositions and a novel structural theorem that generalizes a theorem in Mukhopadhyay-Nanongkai [STOC'20] and , in turn, helps simplify their algorithms .
After revision:  At the heart of our algorithm are a clever routing trick and two structural lemmas regarding the structure of a minimum cut of a graph. These two structural lemmas considerably strengthen and generalize the framework of Mukhopadhyay-Nanongkai [STOC'20] and , in turn, helps simplify their algorithms .