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#F2205. Sereja and Brackets

    ID: 2211 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 6 上传者: 标签>数据结构调度算法思想提高难度共享题库Codeforces英文题面题目来源题面语言

Sereja and Brackets

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 «()(())(())».

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1810 题。保留原作者与原赛事署名。