Changing Brackets
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.
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.
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.
Samples
3
([))[)()][]]
3
1 12
4 9
3 6
))))))
2
2 3
1 4
[]
1
1 2
0
2
1
0
0
0
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.