Let $n$ be postive integer number, and $x_{i}\ge 0$, such $$x_{i}x_{j}\le 4^{-|i-j|},1\le i,j\le n$$ then I have prove $$x_{1}+x_{2}+\cdots+x_{n}<\dfrac{5}{3}$$

Question :

Let $n$ be postive integer number, and $x_{i}\ge 0$, such $$x_{i}x_{j}x_{k}\le 4^{-|i-j-k|},1\le i,j,k\le n$$ then I have prove $$x_{1}+x_{2}+\cdots+x_{n}<C$$ find the best constant $C?$