P180 flight crew reports runway excursion after landing in strong crosswind conditions.

Narrative

Aircraft departed the left side of Runway XXC. I briefed a planned 135 KT approach and 125 KT touchdown for the reported wind conditions as obtained from ATIS; 210 degrees at 10 KTS; gusting to 18 KTS. On short final; the Tower cleared us to land and reported the same winds as on the ATIS report and provided us with a report from a preceding aircraft that had encountered a 10 KT change in airspeed and a 10 KT tailwind on final. Just prior to touchdown; the aircraft experienced a left rear; quartering wind gust that extended our touchdown. Upon touchdown on centerline; with all wheels in contact with the runway; the aircraft yawed sharply to the left and could not be controlled with full right rudder input and the aircraft began to slide. Differential power was momentarily applied; using the left power lever; which was effective in tracking the aircraft back toward centerline. The aircraft again began to yaw sharply to the left and again full rudder input was ineffective. No other corrections were attempted as the aircraft departed the runway. After the aircraft came to rest; we shut down and I ascertained the passenger's condition and we exited the aircraft. There were no injuries to the crew of passenger and no apparent damage to the aircraft.