Sereja and Brackets

Description:

Input:

The first line contains a sequence of characters s₁, s₂, ..., 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.

Sample Input:

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

Sample 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 = s_k1s_k2... s_k|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 «()(())(())».