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In this paper, we propose a novel framework for multilevel full-chip routing considering both routability and performance called MR. The two-stage multilevel framework consists of coarsening, followed by uncoarsening. Unlike the previous multilevel routing, MR integrates global routing, detailed routing, and resource estimation, together at each level of the framework, leading to more accurate routing resource estimation during coarsening and thus facilitating the solution refinement during uncoarsening. Further, the exact routing information obtained at each level makes MR more flexible in dealing with various routing objectives (such as crosstalk, power, etc.). Experimental results show that MR obtains significantly better routing solutions than previous works. For example, for a set of 11 commonly used benchmark circuits, MR achieves 100% routing completion for all circuits, while the previous multilevel routing, the three-level routing, and the hierarchical routing can complete routing for only 2, 0, 2 circuits, respectively. In particular, the number of routing layers used by MR is even smaller. We also have performed experiments on timing-driven routing. The results are also very promising.