Sereja and Brackets

- 本题中「合法括号串」的定义如下： - 空串是「合法括号串」。 - 若 $s$ 是「合法括号串」，则 $(s)$ 是「合法括号串」。 - 若 $s,t$ 是「合法括号串」，则 $st$ 是「合法括号串」。 - 有一个括号串 $s$。$m$ 次操作。操作有一种： 1. `l r`：求字符串 $t=s_ls_{l+1}\cdots s_r$ 的所有 **子序列** 中，长度最长的「合法括号串」，输出长度即可。 - $1\le |s|\le 10^6$，$1\le m\le 10^5$。

Sereja has a bracket sequence $ s_{1},s_{2},...,s_{n} $ , or, in other words, a string $ s $ of length $ n $ , consisting of characters "(" and ")". Sereja needs to answer $ m $ queries, each of them is described by two integers $ l_{i},r_{i} $ $ (1<=l_{i}<=r_{i}<=n) $ . The answer to the $ i $ -th query is the length of the maximum correct bracket subsequence of sequence $ s_{li},s_{li}+1,...,s_{ri} $ . Help Sereja answer all queries. You can find the definitions for a subsequence and a correct bracket sequence in the notes.

The first line contains a sequence of characters $ s_{1},s_{2},...,s_{n} $ $ (1<=n<=10^{6}) $ without any spaces. Each character is either a "(" or a ")". The second line contains integer $ m $ $ (1<=m<=10^{5}) $ — the number of queries. Each of the next $ m $ lines contains a pair of integers. The $ i $ -th line contains integers $ l_{i},r_{i} $ $ (1<=l_{i}<=r_{i}<=n) $ — the description of the $ i $ -th query.

Print the answer to each question on a single line. Print the answers in the order they go in the input.

())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10

0
0
2
10
4
6
6

A subsequence of length $ |x| $ of string $ s=s_{1}s_{2}...\ s_{|s|} $ (where $ |s| $ is the length of string $ s $ ) is string $ x=s_{k1}s_{k2}...\ s_{k|x|} $ $ (1<=k_{1}<k_{2}<...<k_{|x|}<=|s|) $ . A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not. For the third query required sequence will be «()». For the fourth query required sequence will be «()(())(())».