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It will draft much better if you go up through the roof. You can get a spacer/roof flange to keep it away from the wood. You can also vent it through the wall then go up the sidewall to above the roof but it will take much longer for the flue to heat up in cold weather and it's the heat rising in the flue that creates the draft.
Also, whatever way you go the flue must terminate at least 2' above anything within 10' measured horizontally