TOKYO, Sept 1 (Reuters) - Japan's Nikkei stock average drifted higher on Tuesday in choppy trade, helped by gains in Shanghai shares although rises were limited by the yen's advance against the dollar. The benchmark Nikkei rose 0.4 percent or 37.53 points points to 10,530.06 after drifting in and out of negative territory during early trade. The broader Topix rose 0.3 percent to 968.77. (Reporting by Elaine Lies)