CF1593G Changing Brackets

A sequence of round and square brackets is given. You can change the sequence by performing the following operations: 1. change the direction of a bracket from opening to closing and vice versa without changing the form of the bracket: i.e. you can change '(' to ')' and ')' to '('; you can change '\[' to '\]' and '\]' to '\['. The operation costs $ 0 $ burles. 2. change any square bracket to round bracket having the same direction: i.e. you can change '\[' to '(' but not from '(' to '\['; similarly, you can change '\]' to ')' but not from ')' to '\]'. The operation costs $ 1 $ burle. The operations can be performed in any order any number of times. You are given a string $ s $ of the length $ n $ and $ q $ queries of the type "l r" where $ 1 \le l < r \le n $ . For every substring $ s[l \dots r] $ , find the minimum cost to pay to make it a correct bracket sequence. It is guaranteed that the substring $ s[l \dots r] $ has an even length. The queries must be processed independently, i.e. the changes made in the string for the answer to a question $ i $ don't affect the queries $ j $ ( $ j > i $ ). In other words, for every query, the substring $ s[l \dots r] $ is given from the initially given string $ s $ . A correct bracket sequence is a sequence that can be built according the following rules: - an empty sequence is a correct bracket sequence; - if "s" is a correct bracket sequence, the sequences "(s)" and "\[s\]" are correct bracket sequences. - if "s" and "t" are correct bracket sequences, the sequence "st" (the concatenation of the sequences) is a correct bracket sequence. E.g. the sequences "", "(()\[\])", "\[()()\]()" and "(())()" are correct bracket sequences whereas "(", "\[(\])" and ")))" are not.

The first line contains one integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Then $ t $ test cases follow. For each test case, the first line contains a non-empty string $ s $ containing only round ('(', ')') and square ('\[', '\]') brackets. The length of the string doesn't exceed $ 10^6 $ . The string contains at least $ 2 $ characters. The second line contains one integer $ q $ ( $ 1 \le q \le 2 \cdot 10^5 $ ) — the number of queries. Then $ q $ lines follow, each of them contains two integers $ l $ and $ r $ ( $ 1 \le l < r \le n $ where $ n $ is the length of $ s $ ). It is guaranteed that the substring $ s[l \dots r] $ has even length. It is guaranteed that the sum of the lengths of all strings given in all test cases doesn't exceed $ 10^6 $ . The sum of all $ q $ given in all test cases doesn't exceed $ 2 \cdot 10^5 $ .

For each test case output in a separate line for each query one integer $ x $ ( $ x \ge 0 $ ) — the minimum cost to pay to make the given substring a correct bracket sequence.

Consider the first test case. The first query describes the whole given string, the string can be turned into the following correct bracket sequence: "(\[()\])()\[\[\]\]". The forms of the brackets aren't changed so the cost of changing is $ 0 $ . The second query describes the substring ")\[)()\]". It may be turned into "(()())", the cost is equal to $ 2 $ . The third query describes the substring "))\[)". It may be turned into "()()", the cost is equal to $ 1 $ . The substrings of the second test case contain only round brackets. It's possible to prove that any sequence of round brackets having an even length may be turned into a correct bracket sequence for the cost of $ 0 $ burles. In the third test case, the single query describes the string "\[\]" that is already a correct bracket sequence.