reconstructing LOB from NASDAQ ITCH feed - cross trade messages

Hi,

I am trying to reconstruct the limit order book from the NASDAQ ITCH 4.1 feed, and am confused on how to treat the cross trade messages ("Q").

Do these orders impact the limit order book? How?
If they do, how would one go about updating the order book from them - given that these messages provide no order ID or the direction (buy/sell) of the cross trade?

Thanks a lot!
 
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