A321 Captain reported the complete loss of pressurization during cruise. Flight descended and continued to destination.

Narrative

While at 35;000 feet; over City X ; enroute to ZZZ; we had a Cabin Pressure System 1 & 2 fault. The ECAM and QRH were completed per SOP. The pressure system was put into the manual mode IAW (In Accordance With) the ECAM and QRH. Cabin pressure stabilized at target altitude of 6500 feet (per the ECAM system status page). Maintenance Control confirmed via Satcom all steps were completed and flight could continue to ZZZ.CA and FO took their last bathroom break. CA briefed FA #1 of situation and warned if the manual mode failed a rapid descent would be required. #1 FA briefed the FA Team of the non-normal. 30 nm east of ZZZ1 the cabin pressurization rapidly increased to approximately 17;000 ft with an associated ECAM warning. CA and FO executed memory items and FO executed a rapid descent. Requested priority handling and an initial clearance to 12000' was approved by ZZZ center. FO flew the rapid descent IAW the Manual while the CA completed items on the ECAM and QRH. The FAs did an excellent job maintaining professionalism in the cabin. All cabin masks were deployed properly per A321 Manual. No injuries in the cabin and all passengers were calm. Aircraft was cleared to 10;000' and routed via vector airway to ZZZ for a normal ILS runway XXR. Aircraft landed and taxied back to gate. No issues.