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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class SegmentTreeBracket2 {
    private static String s;
    private static int[] valids;
    private static int[] leftBrackets;
    private static int[] rightBrackets;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        s = sc.next();
        int n = sc.nextInt();
        valids = new int[4 * s.length()];
        leftBrackets = new int[4 * s.length()];
        rightBrackets = new int[4 * s.length()];

        build(1, 0, s.length());

        for (int i = 0; i < n; i++) {
            // 1<=left<=right<=n
            int left = sc.nextInt();
            int right = sc.nextInt();
            out.println(getValids(left - 1, right, 1, 0, s.length()).valids);
        }
        out.close();
    }

    // [left, right)
    private static void build(int id, int left, int right) {
        if (left + 1 == right) {
            if (s.charAt(left) == '(')
                leftBrackets[id]++;
            else
                rightBrackets[id]++;
            return;
        }

        int mid = (left + right) / 2;
        build(id * 2, left, mid);
        build(id * 2 + 1, mid, right);

        int min = Math.min(leftBrackets[id * 2], rightBrackets[id * 2 + 1]);
        valids[id] = valids[id * 2] + valids[id * 2 + 1] + 2 * min;
        leftBrackets[id] = leftBrackets[id * 2] - min
                + leftBrackets[id * 2 + 1];
        rightBrackets[id] = rightBrackets[id * 2] + rightBrackets[id * 2 + 1]
                - min;
    }

    // [left, right)
    private static Valid getValids(int x, int y, int id, int left, int right) {
        if (right <= x || left >= y)
            return new Valid(0, 0, 0);
        if (left >= x && right <= y)
            return new Valid(valids[id], leftBrackets[id], rightBrackets[id]);

        int mid = (left + right) / 2;
        Valid validLeft = getValids(x, y, id * 2, left, mid);
        Valid validRight = getValids(x, y, id * 2 + 1, mid, right);
        Valid res = new Valid(0, 0, 0);
        int min = Math.min(validLeft.leftBrackets, validRight.rightBrackets);
        res.valids = validLeft.valids + validRight.valids + 2 * min;
        res.leftBrackets = validLeft.leftBrackets - min
                + validRight.leftBrackets;
        res.rightBrackets = validLeft.rightBrackets + validRight.rightBrackets
                - min;
        return res;
    }

    private static class Valid {
        int valids;
        int leftBrackets;
        int rightBrackets;

        public Valid(int valids, int leftBrackets, int rightBrackets) {
            this.valids = valids;
            this.leftBrackets = leftBrackets;
            this.rightBrackets = rightBrackets;
        }
    }

    // -----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}