Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems. ×

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 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 l i, s l i + 1, ..., s r i. 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 s 1, s 2, ..., s n (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 l i, r i (1 ≤ l i ≤ r i ≤ 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
())(())(())(71 12 31 21 128 125 112 10
Output
00210466
Note

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 k 1 s k 2... 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 «()(())(())».