Linear Models — estimates in alternating sign model

Consider the model $Y_i = \alpha + (-1)^i\beta + u_i$ for all $i = 1, 2, 3, …, 2n$. $u_i$'s are independent random variables with $\mathbb{E}(u_i) = 0$ and $V(u_i) = \sigma^2$ for all $i$. The least squares estimators of $\alpha$ and $\beta$ are given by: I. $\hat{\alpha} = \frac{1}{2n}\sum_{i=1}^{2n}Y_i$ II. $\hat{\beta} = \frac{1}{2n}\left[\sum_{i=1}^{n}Y_{2i} - \sum_{i=1}^{n}Y_{2i-1}\right]$ Which of the statements given above is/are correct?