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TOKYO, Dec 25 (Reuters) - Japan's Nikkei share average rose on Tuesday as exporters gained on a weaker yen, but volume was thin due to a lack of participants during the Christmas holiday. By the midday break, the Nikkei was up 1.3 percent at 10,066.61. Exporters led the gains, with Honda Motor Co adding 1.3 percent, Fanuc Ltd rising 2.3 percent and Canon Inc rising 2.4 percent. Tuesday's buying may have run its course as the holiday doldrums set in, analysts said, but profit-taking should be limited as the weak yen was bolstering sentiment. "Today's participants are not trading aggressively, but as long as the yen stays weak, the market may keep up its strength throughout the day," said Takuya Takahashi, a strategist at Daiwa Securities. The dollar last traded at 84.71 yen, having risen as high as 84.965 yen on Tuesday morning, its best level since April 2011. A weak yen boosts exporters' overseas earnings when repatriated. "Ongoing optimism about the weak yen is lifting hopes that exporters' earnings will be better than expected," said Hiroichi Nishi, general manager at SMBC Nikko Securities. Shinzo Abe, who is set to become prime minister on Wednesday, renewed pressure on the Bank of Japan to adopt a higher inflation target. Abe said he would try to revise a law guaranteeing the BOJ's independence if his demand for a binding 2 percent inflation target - double its current goal - is not met. But analysts also said that a correction may be possible in the next few days as the Japanese market has become overbought. After rising 16.2 percent over the last six weeks, hitting a nine-month high last Friday, the Nikkei is in "overbought" territory, with its 14-day relative strength index at 72.34, above 70 which is deemed the overbought threshold and signalling that a correction may be imminent. The broader Topix gained 0.9 percent to 839.79 in thin trading, with 1.23 billion shares changing hands by the midday break. That compares with last week's average daily trading volume of 3.53 billion shares.