CN-SMO 2014 Problem 4

Let $x_1,x_2,\cdots,x_n$ be non-negative real numbers such that $x_ix_j\le 4^{-|i-j|}$ $(1\le i,j\le n)$ . Prove that$$x_1+x_2+\cdots+x_n\le \frac{5}{3}.$$