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The area-input/output (I/O) flip-chip package provides a high chip-density solution to the demand of more I/Os in very large scale integration designs; it can achieve smaller package size, shorter wirelength, and better signal and power integrity. In this paper, we introduce the routing problem for chip and package co-design and present the first work in the literature to handle the multiple re-distribution layer (RDL) routing problem (without RDL vias) for flip-chip designs, considering pin and layer assignment, signal integrity, signal-skew and total wirelength minimization, and chip-package co-design. Our router adopts a two-stage technique of global routing followed by RDL routing. The global routing assigns each block port to a unique bump pad via an I/O pad and decides the RDL routing among I/O pads and bump pads. Based on the minimum-cost maximum-flow algorithm, we can guarantee 100% RDL routing completion after the assignment and the optimal solution with the minimum wirelength. The RDL routing efficiently distributes the routing points between two adjacent bump pads and then generates a 100% routable sequence to complete the routing. Experimental results based on 12 industry designs demonstrate that our router can achieve 100% routability and the optimal routing wirelength under reasonable central processing unit times, while related works cannot.