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i don't understand kanji+i =

i don't understand
kanji+i = i-adjective
kirei, kirai = na-adjective
all the rest = na-adjective

but suki 好き is a kanji and a hiragana
so it shoudl be an i-adjective
and yet you use 'na' in your example! 好きな
so i really don't understand when you know you have a na- or i-adjective
and why no list included? now i only know 4 japanese adjectives
kirei kirai suki and takai.
no lists?