Steenrod squares on integer cohomology classes.

Question

I know that Steenrod squares are defined as maps $Sq^k \colon H^n(X;\mathbb Z_2) \to H^{n+k}(X,\mathbb Z_2)$. But I often read papers where the $Sq^2 \colon H^n(X;\mathbb Z) \to H^{n+2}(X,\mathbb Z_2)$. What does this mean? Does it mean that I have to precompose the mod $2$ homomorphism $H^n(X,\mathbb Z) \to H^n(X,\mathbb Z_2)$?