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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (PloadyFree@gmail.com)
 */
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);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            Tree tree = new Tree(in.next().toCharArray());
            int q = in.readInt();
            while (q-- > 0) {
                out.printLine(tree.get(in.readInt() - 1, in.readInt() - 1).full * 2);
            }
        }

        class Tree {
            TaskC.Triple[] tree;
            int n;

            Tree(char[] s) {
                int log = 0;
                while (1 << log < s.length) {
                    log++;
                }
                n = 1 << log;

                int nodeCount = n << 1;
                tree = new TaskC.Triple[nodeCount];
                for (int i = 0; i < s.length; i++) {
                    tree[i + n] = s[i] == '('
                            ? new TaskC.Triple(1, 0, 0)
                            : new TaskC.Triple(0, 1, 0);
                }
                for (int i = s.length; i < n; i++) {
                    tree[i + n] = new TaskC.Triple(0, 0, 0);
                }
                for (int i = n - 1; i >= 1; i--) {
                    tree[i] = TaskC.Triple.merge(tree[i * 2], tree[i * 2 + 1]);
                }
            }

            TaskC.Triple get(int from, int to) {
                return get(1, 0, n - 1, from, to);
            }

            TaskC.Triple get(int v, int left, int right, int from, int to) {
                if (to < left || from > right) {
                    return new TaskC.Triple(0, 0, 0);
                }
                if (from <= left && right <= to) {
                    return tree[v];
                }
                int middle = (left + right) >> 1;
                TaskC.Triple l = get(v * 2, left, middle, from, to);
                TaskC.Triple r = get(v * 2 + 1, middle + 1, right, from, to);
                return TaskC.Triple.merge(l, r);
            }

        }

        static class Triple {
            int open;
            int close;
            int full;

            Triple(int open, int close, int full) {
                this.open = open;
                this.close = close;
                this.full = full;
            }

            static TaskC.Triple merge(TaskC.Triple l, TaskC.Triple r) {
                int newFull = Math.min(l.open, r.close);
                return new TaskC.Triple(
                        l.open + r.open - newFull,
                        l.close + r.close - newFull,
                        l.full + r.full + newFull);
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

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

        public void printLine(int i) {
            writer.println(i);
        }

    }
}

