Changing Brackets

2000ms

262144K

Description:

A sequence of round and square brackets is given. You can change the sequence by performing the following operations:

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.
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.

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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.

Sample Input:

3
([))[)()][]]
3
1 12
4 9
3 6
))))))
2
2 3
1 4
[]
1
1 2

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1593G