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.
输入描述:
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.
输出描述:
Print the answer to each question on a single line. Print the answers in the order they go in the input.
示例1
输入
())(())(())(<br />7<br />1 1<br />2 3<br />1 2<br />1 12<br />8 12<br />5 11<br />2 10<br />
输出
0<br />0<br />2<br />10<br />4<br />6<br />6<br />
备注:
A subsequence of length x of string s = s1s2... ss (where s is the length of string s) is string x = sk1sk2... skx(1 ≤ k1 k2 kx ≤ 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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