Consider a scenario where for a given input $\mathbf{x}$, there are only two possible outputs, $\mathbf{y}_1$ and $\mathbf{y}_2$. A reference model assigns probabilities $\pi_{\text{ref}}(\mathbf{y}_1|\mathbf{x}) = 0.6$ and $\pi_{\text{ref}}(\mathbf{y}_2|\mathbf{x}) = 0.4$. A reward function gives scores $r(\mathbf{x}, \mathbf{y}_1) = 2$ and $r(\mathbf{x}, \mathbf{y}_2) = 1$. Assuming the scaling factor $\beta$ is 1, what is the value of the normalization factor $Z(\mathbf{x})$