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tokens: H.K. thanks Takeru Suzuki for inputs to develop the Heyney code and Takashi Noguchi for fruitful discussion about double-diffusive convection. This work was supported by Grants-in-Aid from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) (23244027 and 23103005). H.K. was supported by JSPS KAKENHI Grant Number 15J09448.