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to be indelibly stained or ingrained; to be dyed in deeply
たばこの煙が服に染み付いた。
Cigarette smoke clung to my clothes.
体に染み付いている習慣は変えにくい。
Habits that have become ingrained in the body are hard to change.
この臭いは染み付かないように注意してください。
Please be careful not to let this smell get into your clothes.