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 «()(())(())».

import java.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

import static java.lang.Math.min;

public class SerejaAndBrackets implements Closeable {

    private InputReader in = new InputReader(System.in);
    private PrintWriter out = new PrintWriter(System.out);

    private class Node {
        private int lo, hi, open, close, result;

        private void merge(Node left, Node right) {
            int tmp = min(left.open, right.close);
            result = left.result + right.result + tmp;
            open = left.open + right.open - tmp;
            close = left.close + right.close - tmp;
        }
    }

    private class SegmentTree {
        private char[] x;
        private Node[] nodes;

        private SegmentTree(char[] x) {
            this.x = x;
            int n = x.length;
            nodes = new Node[4 * n + 1];
            for (int i = 0; i < nodes.length; i++) {
                nodes[i] = new Node();
            }
            init(1, 0, n - 1);
        }

        private void init(int idx, int left, int right) {
            nodes[idx].lo = left;
            nodes[idx].hi = right;
            if (left == right) {
                if (x[left] == '(') {
                    nodes[idx].open = 1;
                } else {
                    nodes[idx].close = 1;
                }
            } else {
                int mid = (left + right) / 2;
                init(idx << 1, left, mid);
                init(idx << 1 | 1, mid + 1, right);
                nodes[idx].merge(nodes[idx << 1], nodes[idx << 1 | 1]);
            }
        }

        private Node query(int idx, int left, int right) {
            if (nodes[idx].lo > right || nodes[idx].hi < left) return new Node();
            if (nodes[idx].lo >= left && nodes[idx].hi <= right) return nodes[idx];

            Node result = new Node();
            Node l = query(idx << 1, left, right);
            Node r = query(idx << 1 | 1, left, right);
            result.merge(l, r);
            return result;
        }
    }

    public void solve() {
        char[] x = in.next().toCharArray();
        SegmentTree tree = new SegmentTree(x);
        int q = in.ni();
        while (q-- > 0) {
            int left = in.ni() - 1, right = in.ni() - 1;
            out.println(tree.query(1, left, right).result << 1);
        }
    }

    @Override
    public void close() throws IOException {
        in.close();
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

        public void close() throws IOException {
            reader.close();
        }
    }

    public static void main(String[] args) throws IOException {
        try (SerejaAndBrackets instance = new SerejaAndBrackets()) {
            instance.solve();
        }
    }
}
