Consider the three-element Heyting algebra $H = \{0, \frac{1}{2}, 1\}$ ordered by $0 < \frac{1}{2} < 1$. In any Heyting algebra, the implication operation is defined by $x \to y = \sup \{z \in H \mid x \land z \le y\}$. For the valuation $v(P) = \frac{1}{2}$ and $v(Q) = 0$, what is the valuation of the formula: $\phi = ((P \to Q) \to P) \to P$