  In this paper, we show that for any sequence ${\bf a}=(a_n)_{n\in \Z}\in
\{1,\ldots,k\}^\mathbb{Z}$ and any $\epsilon>0$, there exists a Toeplitz
sequence ${\bf b}=(b_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ such that the
entropy $h({\bf b})\leq 2 h({\bf a})$ and
$\lim_{N\to\infty}\frac{1}{2N+1}\sum_{n=-N}^N|a_n-b_n|<\epsilon$. As an
application of this result, we reduce Sarnak Conjecture to Toeplitz systems,
that is, if the M\"{o}bius function is disjoint from any Toeplitz sequence with
zero entropy, then the Sarnak conjecture holds.
