Polynomial size Boolean circuit for counting number of bits

Question

Given a natural number $n \geq 1$, I am looking for a Boolean circuit over $2n$ variables, $\varphi(x_1, y_1, \dots, x_n, y_n)$, such that the output is true if and only if the assignment that makes it true verifies

$$\sum_{i = 1}^{i = n} (x_i + y_i) \not\equiv n \bmod 3$$

I should specify that this I am looking for a Boolean circuit, not necessarily a Boolean formula as it is usually written in Conjunctive Normal Form (CNF). This is because when written in CNF, a formula like the one before has a trivial representation where the number of clauses is approximately $\frac{4^n}{3}$, as it contains a clause for every assignment $(x_1, y_1, \dots, x_n, y_n)$ whose bits sum to a value which is congruent with $n \bmod 3$. Constructing such a formula would therefore take exponential time.

I have been told that a Boolean circuit can be found for this formula that accepts a representation of size polynomial in $n$. However, so far I have been unable to find it. I would use some help; thanks.