Let \(n \geqslant 3\) be an integer, and let \(x_1,x_2,\ldots,x_n\) be real numbers in the interval \([0,1]\). Let \(s=x_1+x_2+\ldots+x_n\), and assume that \(s \geqslant 3\). Prove that there exist integers \(i\) and \(j\) with \(1 \leqslant i<j \leqslant n\) such that

\[2^{j-i}x_ix_j>2^{s-3}.\]