The Japanese Nikkei 225 index hit a record during Tuesday trading, as the stock market continued to rise after Japan's Prime Minister Shigeru Ishiba announced over the weekend that he is stepping down.
The index fell slightly from the absolute record level, but by lunchtime it had still risen by 0.2 percent. The broader Topix index also showed positive figures, up 0.1 percent.
Hong Kong's Hang Seng index rose more, and was up 1.5 percent after some hours of trading.
Shanghai's composite index also went up, 0.1 percent, while Shenzhen's equivalent fell 0.4 percent.
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