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The sentence as it stands doesn't seem to mean anything. "left cut" is the problem. Do you mean maybe "left out"? "left cut" is not any English I am familiar with. If you want explanation of a sentence, please give a sentence or two before and one after, so we can see the context. "counted" is pretty much the same as "was important". If it's actually "left out", it would mean something like "He only kept the stuff that was not important".