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.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;
import java.util.ArrayList;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class ProblemCSerejaAndBrackets {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            String s = in.next();
            ArrayList<int[]>[] query = new ArrayList[s.length() + 1];
            for (int i = 0; i <= s.length(); i++) {
                query[i] = new ArrayList<>();
            }
            int m = in.nextInt();
            long[] ans = new long[m];
            for (int i = 0; i < m; i++) {
                int L = in.nextInt(), R = in.nextInt();
                query[R].add(new int[]{L, i});
            }
            FenwickTree fw = new FenwickTree(s.length() + 1);
            Stack<Integer> st = new Stack<>();
            for (int i = 1; i <= s.length(); i++) {
                if (s.charAt(i - 1) == '(') {
                    st.add(i);
                } else if (!st.empty()) {
                    fw.add(st.pop(), 1);
                }
                for (int[] x : query[i]) {
                    ans[x[1]] = fw.query(x[0], i);
                }
            }
            for (long x : ans) {
                out.println(x * 2);
            }
        }

    }

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

    }

    static class FenwickTree {
        long[] data;

        public FenwickTree(int n) {
            data = new long[n];
        }

        public void add(int at, long value) {
            for (int i = at; i < data.length; i += (i & -i)) {
                data[i] += value;
            }
        }

        public long query(int at) {
            long res = 0;
            for (int i = at; i > 0; i -= (i & -i)) {
                res += data[i];
            }
            return res;
        }

        public long query(int from, int to) {
            return query(to) - query(from - 1);
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream out) {
            super(out);
        }

        public OutputWriter(Writer out) {
            super(out);
        }

        public void close() {
            super.close();
        }

    }
}

