Tokyo, July 3 (BridgeNews) - Japanese shares ended the morning session higher Tuesday on short covering following Monday's sell off, aided by a positive reaction to a strong U.S. National Association of Purchasing Managers report. The market upside was, however, limited on a lack of follow-through buying. The Nikkei 225 Stock Average rose 76.12 points, or 0.6%, to 12,827.30.