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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            String s = in.next();
            int m = in.nextInt();
            TaskC.SegTree seg = new TaskC.SegTree(s);

            for (int i = 0; i < m; i++) {
                int l = in.nextInt();
                int r = in.nextInt();
                out.println(2 * seg.query(1, 0, s.length() - 1, l - 1, r - 1).a);
            }
        }

        static class trip {
            int a;
            int b;
            int c;

            trip(int a1, int b1, int c1) {
                a = a1;
                b = b1;
                c = c1;
            }

        }

        static class SegTree {
            TaskC.trip[] seg;

            SegTree(String s) {
                seg = new TaskC.trip[4 * s.length()];
                build(s, 1, 0, s.length() - 1);
            }

            void build(String s, int v, int tl, int tr) {
                if (tl == tr) {
                    if (s.charAt(tl) == '(') seg[v] = new TaskC.trip(0, 1, 0);
                    else seg[v] = new TaskC.trip(0, 0, 1);
                } else {
                    int tm = (tl + tr) / 2;
                    build(s, v * 2, tl, tm);
                    build(s, v * 2 + 1, tm + 1, tr);
                    int t = Math.min(seg[v * 2].b, seg[v * 2 + 1].c);
                    seg[v] = new TaskC.trip(seg[v * 2].a + seg[v * 2 + 1].a + t, seg[v * 2].b + seg[v * 2 + 1].b - t, seg[v * 2].c + seg[v * 2 + 1].c - t);
                }
            }

            TaskC.trip query(int v, int tl, int tr, int l, int r) {
                if (l > r)
                    return new TaskC.trip(0, 0, 0);
                if (l == tl && r == tr)
                    return seg[v];
                int tm = (tl + tr) / 2;
                TaskC.trip left = query(v * 2, tl, tm, l, Math.min(r, tm));
                TaskC.trip right = query(v * 2 + 1, tm + 1, tr, Math.max(l, tm + 1), r);
                int t = Math.min(left.b, right.c);

                return new TaskC.trip(left.a + right.a + t, left.b + right.b - t, left.c + right.c - t);
            }

        }

    }

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

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private void fillTokenizer() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            fillTokenizer();
            return tokenizer.nextToken();
        }

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

    }
}

