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5830: Sereja and Brackets

内存限制：256 MB 时间限制：2 S 标准输入输出
题目类型：传统 评测方式：文本比较 上传者：
提交：1 通过：1
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题目描述

C. Sereja and Brackets
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Sereja has a bracket sequence s1,s2,...,sn, 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 li,ri (1≤li≤ri≤n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence sli,sli+1,...,sri. Help Sereja answer all queries.
You can find the definitions for a subsequence and a correct bracket sequence in the notes.
Input
The first line contains a sequence of characters s1,s2,...,sn (1≤n≤106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1≤m≤105) − the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers li,ri (1≤li≤ri≤n) − the description of the i-th query.
Output
Print the answer to each question on a single line. Print the answers in the order they go in the input.
Examples
Input 
())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10
Output 
0
0
2
10
4
6
6
Note
A subsequence of length |x| of string s=s1s2... s|s| (where |s| is the length of string s) is string x=sk1sk2... sk|x| (1≤k1<k2<...<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 «()(())(())».

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