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.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author unknown
 */
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);
        CSerejaAndBrackets solver = new CSerejaAndBrackets();
        solver.solve(1, in, out);
        out.close();
    }

    static class CSerejaAndBrackets {
        Node[] st;
        int n;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            String s = in.nextString();
            n = s.length();
            st = new Node[2 * n];
            build(s);
            int q = in.nextInt();
            while (q-- > 0) {
                int l = in.nextInt();
                int r = in.nextInt();
                out.println(queryRange(--l, --r));
            }
        }

        int queryRange(int l, int r) {
            Node resl = new Node();
            Node resr = new Node();
            r += n;
            l += n;
            while (l <= r) {
                if ((l & 1) == 1) {
                    resl = combine(resl, st[l]);
                }
                if ((r & 1) != 1) {
                    resr = combine(st[r], resr);
                }
                l++;
                r--;
                l >>= 1;
                r >>= 1;
            }
            return combine(resl, resr).v * 2;
        }

        void build(String s) {
            for (int i = 0; i < 2 * n; i++) {
                st[i] = new Node();
            }
            for (int i = 2 * n - 1; i > 0; i--) {
                if (i >= n) {
                    if (s.charAt(i - n) == '(') {
                        st[i].o = 1;
                    } else {
                        st[i].c = 1;
                    }
                } else {
                    st[i] = combine(st[2 * i], st[2 * i + 1]);
                }
            }
        }

        Node combine(Node lnode, Node rnode) {
            Node comb = new Node();
            int temp = _F.min(lnode.o, rnode.c);
            comb.v = lnode.v + rnode.v + temp;
            comb.c = lnode.c + rnode.c - temp;
            comb.o = lnode.o + rnode.o - temp;
            return comb;
//        int temp = min(st[2*i].o,st[2*i+1].c);
//        st[i].v=st[2*i].v+st[2*i+1].v+temp;
//        st[i].c= st[2*i].c+st[2*i+1].c-temp;
//        st[i].o =st[2*i].o + st[2*i+1].o-temp;
        }

        class Node {
            int v;
            int o;
            int c;

        }

    }

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

        }

    }

    static class _F {
        public static <T extends Comparable<T>> T min(T... list) {
            T candidate = list[0];
            for (T i : list) {
                if (candidate.compareTo(i) > 0) {
                    candidate = i;
                }
            }
            return candidate;
        }

    }

    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 println(long i) {
            writer.println(i);
        }

    }
}

