\gdef\thisproblemauthor{Ivan Kazmenko}
\gdef\thisproblemdeveloper{Ivan Kazmenko}
\begin{problem}{Bracket Expression}
{bracket-expression.in}{bracket-expression.out}
{2 seconds (\textsl{3 seconds for Java})}{256 mebibytes}{}

In this problem, you have to find the number corresponding to a given
bracket expression.

\def\S{\mathcal{S}}

As you may already know, the set of
\textit{regular bracket sequences} $\S$
is recursively defined as follows:

\begin{enumerate}
\item $\varepsilon \in \S$ (empty sequence)
\item $A \in \S \Rightarrow \texttt{(}A\texttt{)} \in \S$ (bracketing)
\item $A, B \in \S \Rightarrow AB \in \S$ (concatenation)
\end{enumerate}

For example, $\text{``}\texttt{(())}\text{''} \in \S$ by rule $2$
and the fact that $\text{``}\texttt{()}\text{''} \in \S$; this, in turn,
follows by rule $2$ from the fact that $\text{``}\text{''} \in \S$;
the latter is simply rule $1$.
Similarly, $\text{``}\texttt{()()}\text{''} \in \S$ by rule $3$
and the fact that $\text{``}\texttt{()}\text{''} \in \S$;
the latter is proven above.

We assign a number $f (X)$ to every regular bracket sequence $X \in \S$
as follows:

\begin{enumerate}
\item $\varepsilon \longrightarrow 1$
\item $\texttt{(}A\texttt{)} \longrightarrow 1 + f (A)$
\item $AB \longrightarrow f (A) \cdot f (B)$
\end{enumerate}

It can be shown that this assignment is proper because it does not depend
on the order of calculation.
Note that the same number can be assigned to different sequences.

Given a regular bracket sequence, find the number assigned to it.

\InputFile

The first line of input contains an expression which consists
of opening (``\texttt{(}'') and closing (``\texttt{)}'') brackets
and has length from $0$ to $40$ characters, inclusive.
It is guaranteed that this expression represents a regular bracket sequence.

\OutputFile

On the only line, print the number assigned to the given expression.

\Examples

\begin{example}
\exmp{
(())
}{
3
}%
\exmp{
()()
}{
4
}%
\end{example}

\Explanations

In the first example, the expression <<\texttt{(())}>> is assigned
the number $(1 + 1) + 1 = 3$.

In the second example, the expression <<\texttt{()()}>> is assigned
the number $(1 + 1) \cdot (1 + 1) = 2 \cdot 2 = 4$.

\end{problem}
