The Fibonacci sequence is determined by conditions $ F_0 = 0, F1 = 1$, and $ F_k=F_{k-1}+F_{k-2}$ for all $ k \ge 2$. Let $ n$ be a positive integer and let $ P(x) = a_mx^m +. . .+ a_1x+ a_0$ be a polynomial that satisfies the following two conditions: (1) $ P(F_n) = F_{n}^{2}$ ; (2) $ P(F_k) = P(F_{k-1}) + P(F_{k-2}$ for all $ k \ge 2$. Find the sum of the coefficients of P.