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

public class Main223B {

    private FastScanner in;
    private PrintWriter out;

    public void solve() throws IOException {
        SegmentTree tree = new SegmentTree(in.next());
        int N = in.nextInt();
        for(int i = 0; i < N; i++) {
            out.println(2 * tree.countSeq(in.nextInt(), in.nextInt()));
        }
    }

    class Node {
        int seqLength;
        int countOpen;
        int countClose;
        int left;
        int right;
        Node leftNode;
        Node rightNode;
    }

    class SegmentTree {
        Node root;
        SegmentTree(String s) {
            root = new Node();
            root.left = 1;
            root.right = s.length();
            initNode(root, s);
        }

        private void initNode(Node node, String s) {
            if(node.left == node.right) {
                if(s.charAt(node.left - 1) == ')') {
                    node.countClose = 1;
                }
                else {
                    node.countOpen = 1;
                }
                return;
            }
            int mid = (node.left + node.right) / 2;
            node.leftNode = new Node();
            node.leftNode.left = node.left;
            node.leftNode.right = mid;
            node.rightNode = new Node();
            node.rightNode.left =mid + 1;
            node.rightNode.right = node.right;
            initNode(node.leftNode, s);
            initNode(node.rightNode, s);
            int addSeq = Math.min(node.leftNode.countOpen, node.rightNode.countClose);
            node.seqLength = node.leftNode.seqLength + node.rightNode.seqLength + addSeq;
            node.countOpen = node.leftNode.countOpen + node.rightNode.countOpen - addSeq;
            node.countClose = node.leftNode.countClose + node.rightNode.countClose - addSeq;
        }

        int countSeq(int left, int right) {
            Res res = countSeqRec(root, left, right);
            return res.seq;
        }

        class Res {
            int seq;
            int open;
            int close;
        }

        Res countSeqRec(Node node, int left, int right) {
            Res res = new Res();
            if(left == node.left && right == node.right) {
                res.open = node.countOpen;
                res.close = node.countClose;
                res.seq = node.seqLength;
                return res;
            }
            if(right <= node.leftNode.right) {
                return countSeqRec(node.leftNode, left, right);
            }
            if(left >= node.rightNode.left) {
                return countSeqRec(node.rightNode, left, right);
            }
            Res resLeft = countSeqRec(node.leftNode, left, node.leftNode.right);
            Res resRight = countSeqRec(node.rightNode, node.rightNode.left, right);
            int addSeq = Math.min(resLeft.open, resRight.close);
            res.seq = resLeft.seq + resRight.seq + addSeq;
            res.open = resLeft.open + resRight.open - addSeq;
            res.close = resLeft.close + resRight.close - addSeq;
            return res;
        }
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {

        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }

    public static void main(String[] arg) {
        new Main223B().run();
    }
}