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TOKYO, April 2 (Reuters) - Japan's Nikkei share average rose on Thursday, rebounding from a three-week low, helped by short-covering and hopes that the central bank is buying stocks. The Nikkei benchmark ended 1.5 percent higher to 19,312.79, posting the biggest daily percentage gain since February 12. The broader Topix gained 1.7 percent to 1,554.17 and the JPX-Nikkei Index 400 also added 1.7 percent to 14,126.63. Central bank data showed that it bought 35.2 billion yen worth of exchange traded funds (ETF) on Wednesday, when the market fell to a three-week low.