The product of dg Lie algebras

Question

I am trying to understand what are products and coproducts in the category of dg Lie algebras. I am okay with coproducts. For products, however, this Wikipedia article says that given $\mathfrak{g},\mathfrak{h}$ two dg Lie algebras, their product is given by the dg Lie algebra with underlying vector space given by the product $\mathfrak{g}\times \mathfrak{h}$ with bracket $$[(x,y),(x',y')] = ([x,y],[x',y'])$$ and differential $$d(x,y) = (dx,dy).$$ My problem is with this differential. It looks to me that it would have degree $-2$ instead of $-1$ as we would like. Am I missing something (such as using the correct grading on $\mathfrak{g}\times\mathfrak{h}$)?