How do we compute the rational cohomology ring $H^*\left(\bigsqcup_{i\ge 1}S^n;\mathbb{Q}\right)$?

Question

How do we compute the rational cohomology ring $H^*\left(\bigsqcup_{i\ge 1}S^n;\mathbb{Q}\right)$?

Thoughts: Clearly, this is $H^*\left(\bigsqcup_{i\ge 1}S^n;\mathbb{Q}\right)\cong \prod_{i\ge 1}H^*(S^n;\mathbb{Q})$. I am not sure where to go from here.

Thanks in advance!