Bracket Sequences

`Problem`
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, where denotes the type of 's bracket (open or close). It is not mandatory that is necessarily correct. Your task is to determine the number of 's such that is a correct bracket sequence.

`Input `
)()()(

`output`
3
`Explanation`
For all i=2,4,6, the shift of string will be ()()(), which is the correct bracket sequence. and the answer is 3