Logic Masters Deutschland e.V.

Oh no! I just solved this word search, but I lost all of the letters. Luckily I know that it only contains the letters a,b,c,d,e,f,g,h,i and all of the letters follow sudoku rules. Each grey rectangle is where I found a word. Words can be in either direction, appear at most once, and not all words are used. Help me find all of the words then fill in the remaining empty cells!

Word Bank:
ace, acid, add, age,
bad, bag, beach, bed, beg, bid, big,
cab, cage, cafe, chef, chief,
dig, deaf, dice,
each,
fed, fig, face, fade,
he, had, hid, head, hag,
ice, idea, if



penpa link: https://git.io/JLN4Y