Showing arrow heads for intermediate chained arrows in \draw (A) -- (B) -- (C) -- (D) -- (E)

Question

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}[flow/.style={thick,-stealth}]

  \node             (A) {A};
  \node[right=of A] (B) {B};
  \node[right=of B] (C) {C};
  \node[right=of C] (D) {D};
  \node[right=of D] (E) {E};

  \draw[flow] (A) -- (B) -- (C) -- (D) -- (E);

\end{tikzpicture}
\end{document}

This code produces the follow layout:

A ---- B ---- C ---- D  ---> E

How can I add an arrow head for each of the intermediate arrows without using separate \draw commands?

A ---> B ---> C ---> D  ---> E