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 ≤ 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.

Input

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.

Output

Print the answer to each question on a single line. Print the answers in the order they go in the input.

Examples

Input

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


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 = 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 «()(())(())».
def main():
    l, x = [0], 0
    for c in raw_input():
        if c == '(':
            x += 1
        else:
            x -= 1
        l.append(x)
    tree = [l]
    while len(l) > 7:
        l = [min(l[_:_ + 8]) for _ in range(0, len(l), 8)]
        tree.append(l)
    res, l = [], tree[0]
    for _ in range(int(raw_input())):
        lo, hi = map(int, raw_input().split())
        lo -= 1
        x = hi - lo - l[lo] - l[hi]
        hi += 1
        tmp = []
        for ll in tree:
            t = (lo + 7) & 0x7FFFFFF8
            if t > hi:
                t = hi
            tmp.extend(ll[lo:t])
            lo = t >> 3
            if t < hi & 0x7FFFFFF8:
                t = hi & 0x7FFFFFF8
            tmp.extend(ll[t:hi])
            hi = t >> 3
        res.append(str(x + min(tmp) * 2))
    print('\n'.join(res))


if __name__ == '__main__':
    main()
