Double Data Trouble II

Suppose that you run linear regression on some dataset and obtain the coefficients $\hat{\beta}_{OLS}$. Recall that if $X$ is the data and $\sigma^2$ is the variance of the IID normal errors, then $\text{Var}\left(\hat{\beta}_{OLS}\right) = \sigma^2(X^TX)^{-1}$. If you were to run linear regression again on the dataset where you duplicate each point in your original dataset and obtain new coefficients $\hat{\beta}_{OLS}'$, find the constant $c$ such that $\text{Var}\left(\hat{\beta}_{OLS}'\right) = c\text{Var}\left(\hat{\beta}_{OLS}\right)$. If no such constant exists, enter $-1$.