H. Higher Order Functions
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Helen studies functional programming and she is fascinated with a concept of higher order functions — functions that are taking other functions as parameters. She decides to generalize the concept of the function order and to test it on some examples.

For her study, she defines a simple grammar of types. In her grammar, a type non-terminal $$$T$$$ is defined as one of the following grammar productions, together with $$$\textrm{order}(T)$$$, defining an order of the corresponding type:

  • "()" is a unit type, $$$\textrm{order}(\textrm{"}\texttt{()}\textrm{"}) = 0$$$.
  • "(" $$$T$$$ ")" is a parenthesized type, $$$\textrm{order}(\textrm{"}\texttt{(}\textrm{"}\,T\,\textrm{"}\texttt{)}\textrm{"}) = \textrm{order}(T)$$$.
  • $$$T_1$$$ "->" $$$T_2$$$ is a functional type, $$$\textrm{order}(T_1\,\textrm{"}\texttt{->}\textrm{"}\,T_2) = max(\textrm{order}(T_1) + 1, \textrm{order}(T_2))$$$. The function constructor $$$T_1$$$ "->" $$$T_2$$$ is right-to-left associative, so the type "()->()->()" is the same as the type "()->(()->())" of a function returning a function, and it has an order of $$$1$$$. While "(()->())->()" is a function that has an order-1 type "(()->())" as a parameter, and it has an order of $$$2$$$.

Helen asks for your help in writing a program that computes an order of the given type.

Input

The single line of the input contains a string consisting of characters '(', ')', '-', and '>' that describes a type that is valid according to the grammar from the problem statement. The length of the line is at most $$$10^4$$$ characters.

Output

Print a single integer — the order of the given type.

Examples
Input
()
Output
0
Input
()->()
Output
1
Input
()->()->()
Output
1
Input
(()->())->()
Output
2
Input
()->(((()->())->()->())->())
Output
3