Bracket String and Queries

A bracket string is a string made of '(' and ')'. A correct bracket string is defined as follows.

1. The empty string is a correct bracket string.
2. If S is a correct bracket string, then (S) is also a correct bracket string.
3. If S and T are correct bracket strings, then ST is also a correct bracket string.
4. Every correct bracket string can be built using only the three rules above.

You are given a bracket string S = s1s2...sN made of '(' and ')', along with M queries. Each query consists of a single integer index, and it means the following.

• If the index-th character of S is '(', change it to ')'; if it is ')', change it to '('.

Queries are applied cumulatively: the i-th query must be applied to the result of applying the (i-1)-th query. Count how many times the result of applying a query is a correct bracket string.

The first line gives the string S. The second line gives the number of queries M. The following M lines give the query index, one per line.

On the first line, print the number of times the result of applying a query was a correct bracket string.

• 1 ≤ |S| ≤ 100,000
• 1 ≤ M ≤ 100,000
• 1 ≤ index ≤ |S|

For S = "()()()()", the results of applying the queries of sample 1 are as follows.

• ((()()()
• ((()()))
• ((((()))
• (((())))
• (()())))
• (()())()
• )()())()
• )))())()