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.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;
import java.util.Stack;

/**
 * Created by lenovo on 3/6/2016.
 */
public class Brackets {
    public static void main(String[] args) throws IOException {
        //Scanner scanner = new Scanner(System.in);
        StringBuilder sb  = new StringBuilder();
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1014*1024);
        String input = br.readLine();
        int n = Integer.parseInt(br.readLine());
        ArrayList<Node> results = new ArrayList<Node>();
        ArrayList<Integer> answer = new ArrayList<Integer>();
        ArrayList<Interval> intervals = new ArrayList<Interval>();
        Stack<Integer> index = new Stack();

        for (int i = 0; i < n; i++) {
            String line = br.readLine();
            String[] split = line.split("\\s");
            int l = Integer.parseInt(split[0]);
            int r = Integer.parseInt(split[1]);
            intervals.add(new Interval(l, r, i));
            answer.add(0);
        }

        Collections.sort(intervals);
        int rightIndex = 0;

        for (int i = 0; i < input.length(); i++)
            results.add(new Node(0, null, null, null));
        Node root = makeTree(results, 0, input.length());

        for (int i = 0; i < input.length(); i++) {
            if (input.charAt(i) == '(') {
                index.push(i);
            } else if (index.size() != 0) {
                int addIndex = index.pop();
                add(results, addIndex);
            }
            while((rightIndex < n) && (intervals.get(rightIndex).right - 1) == i) {
                answer.set(intervals.get(rightIndex).number
                        ,2 * partialSum(results, root, 0, input.length(), intervals.get(rightIndex).left - 1, intervals.get(rightIndex).right));
                rightIndex++;

            }
        }

        for (int i = 0; i < n; i++) {
            sb.append(answer.get(i)).append('\n');
        }
        System.out.println(sb.toString());
    }

    public static Node makeTree(ArrayList<Node> a, int start, int end) {
        int mid = (start + end) / 2;

        if (end - start == 1) {
            return a.get(start);
        }

        Node left = makeTree(a, start, mid);
        Node right = makeTree(a, mid, end);
        Node newNode = new Node(left.value + right.value, right, left, null);
        left.parent = newNode;
        right.parent = newNode;
        return newNode;
    }

    public static void add(ArrayList<Node> a, int index) {
        Node current = a.get(index);
        current.value++;
        while (current.parent != null) {
            current = current.parent;
            current.value++;
        }
    }

    public static int partialSum(ArrayList<Node> a, Node root, int start, int end, int l, int r) {
        int mid = (start + end) / 2;
        int left = 0, right = 0;

        if(start == l && end == r)
            return root.value;

        if (l < mid)
            left = partialSum(a, root.left, start, mid, l, Math.min(mid, r));
        if (r > mid)
            right = partialSum(a, root.right, mid, end, Math.max(mid, l), r);

        return left + right;
    }
}

class Node {
    public int value;
    public Node left;
    public Node right;
    public Node parent;

    public Node(int value, Node right, Node left, Node parent) {
        this.value = value;
        this.left = left;
        this.right = right;
        this.parent = parent;
    }
}

class Interval implements Comparable<Interval>{
    public int left;
    public int right;
    public int number;

    public Interval(int left, int right, int number) {
        this.left = left;
        this.right = right;
        this.number = number;
    }

    @Override
    public int compareTo(Interval o) {
        return this.right - o.right;
    }
}
