C. Sereja and Bracketstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSereja 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.InputThe 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.OutputPrint the answer to each question on a single line. Print the answers in the order they go in the input.ExamplesInput())(())(())(71 12 31 21 128 125 112 10Output00210466NoteA 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 «()(())(())».
Input())(())(())(71 12 31 21 128 125 112 10
Output00210466
['data structures', 'schedules', '*2000']