In a 4-valued Łukasiewicz propositional logic, the set of truth values is $V = \{0, \frac{1}{3}, \frac{2}{3}, 1\}$. The valuation of an implication is defined as $v(A \to B) = \min(1, 1 - v(A) + v(B))$. How many distinct valuations $v: \{P, Q\} \to V$ satisfy the condition $v((P \to Q) \to P) = 1$?