Task: Question Answering
Input (English): Passage: Following the release of With Teeth in 2005, the live band was reassembled for the Live: With Teeth tour.  Since the previous tour five years earlier, much of the band had moved on in their careers, and only drummer Jerome Dillon rejoined. To find replacements, Reznor held auditions during December 2004.  He stated that keyboardist Alessandro Cortini "fit in immediately", though he had trouble finding a guitarist to replace Robin Finck until auditioning Aaron North.
The tour began with a series of small-club performances early in 2005. The band told journalists they were "pleasantly surprised by the interest" of fans despite their lengthy absence.  This initial leg of the tour also included a headlining performance at Coachella Valley Music and Arts Festival.  The band followed with a North American arena tour in autumn 2005, supported by Queens of the Stone Age, Death From Above 1979, Autolux, and Saul Williams. Williams performed on stage with Nine Inch Nails at the Voodoo Music Experience festival during a headlining appearance in hurricane-stricken New Orleans, Reznor's former home. To conclude the With Teeth era of the band, Nine Inch Nails completed a tour of North American amphitheaters in the summer of 2006, joined by Bauhaus, TV on the Radio, and Peaches. The 2007 release Beside You in Time features performances from the North American arena tour, the North American amphitheater tour, and a number of studio rehearsals.Nine Inch Nails were scheduled to perform at the 2005 MTV Movie Awards, but dropped themselves from the show due to a disagreement with the network over the use of an unaltered image of George W. Bush as a backdrop to the band's performance of "The Hand that Feeds". Soon afterwards, Reznor wrote on the official Nine Inch Nails website: "apparently, the image of our president is as offensive to MTV as it is to me".  MTV replied by saying they respected Reznor's point of view, but were "uncomfortable" with the performance being "built around partisan political statements". A performance by the Foo Fighters replaced Nine Inch Nails' time slot on the show.During the first arena performance in 2005, Dillon was forced to stop midway through the show and was subsequently hospitalized.  His condition was later diagnosed as a non-life-threatening cardiac disorder, a consequence of his thyroid medication.  Dillon later remarked that when he was ready to return he encountered "complete apathy and no sympathy" from Reznor and Nine Inch Nails' management. Reznor in turn wrote that Dillon's "recollection of the events leading to his departure from the band is once again inaccurate".  Josh Freese initially replaced Dillon for two shows before Alex Carapetis joined the band for the remainder of the arena tour.  Freese eventually replaced Carapetis and joined the band on a permanent basis. 
Question: What is the full name of the drummer that finished the arena tour after health issues cause the touring drummer to drop out?
Output (English): Alex Carapetis.