A bracket sequence is a string that contains only characters '(' and ')'.

A correct bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences '()()' and '(())' are correct. The resulting expressions of these sequences are: '(1)+(1)' and '((1+1)+1)'. However, '(', ')(', and '(' are incorrect bracket sequences.

You are given a bracket sequence \(s(s_1 s_2 ... s_n)\), where \(s_i\) denotes the type of \(i\)'s bracket (open or close). It is not mandatory that \(s\) is necessarily correct. Your task is to determine the number of \(i\)'s such that \(s_i s_{i+1} ... s_n s_1 s_2 ... s_{i-1}\) is a correct bracket sequence.

Input format

The single line contains sequence \(s\).

Output format

Print the number of shifts denoting the correct bracket sequence.

Constraints

\(|s| \le 5\times 10^5\)