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 TT is defined as one of the following grammar productions, together with order(T)order(T), defining an order of the corresponding type:
“()” is a unit type, order(“()“)=0order(“()”)=0.
“(” TT “)” is a parenthesized type, order(“(“T“)“)=order(T)order(“(“T”)”)=order(T).
T1T1 “->” T2T2 is a functional type, order(T1“->“T2)=max(order(T1)+1,order(T2))order(T1″->”T2)=max(order(T1)+1,order(T2)). The function constructor T1T1 “->” T2T2 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 11. While “(()->())->()” is a function that has an order-1 type “(()->())” as a parameter, and it has an order of 22.
Helen asks for your help in writing a program that computes an order of the given type.
Higher Order Functions solution codeforces
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 104104 characters.
Print a single integer — the order of the given type.