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 \le li \le ri \le 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.

The first line contains a sequence of characters s1,s2,...,sn (1 \le n \le 106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 \le m \le 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 \le li \le ri \le 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.

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 \le k1 \lt k2 \lt ... \lt k|x| \le |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 «()(())(())».