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 Debabrata
 */
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);
        serejaAndBrackets solver = new serejaAndBrackets();
        solver.solve(1, in, out);
        out.close();
    }

    static class serejaAndBrackets {
        static int[] t;
        static int[] o;
        static int[] c;
        static String s;

        public void solve(int testNumber, InputReader scan, OutputWriter out) {
            s = scan.next();
            int n = s.length();
            t = new int[4 * n];
            o = new int[4 * n];
            c = new int[4 * n];

            build(1, 0, n - 1);
            int q = scan.nextInt();
            while (q-- > 0) {
                int a = scan.nextInt() - 1;
                int b = scan.nextInt() - 1;
                out.println((query(1, 0, n - 1, a, b).t) * 2);
            }

        }

        void build(int p, int l, int r) {
            if (r == l) {
                if (s.charAt(l) == '(') {
                    o[p] = 1;
                } else {
                    c[p] = 1;
                }
                return;
            }
            int mid = (l + r) / 2;
            build(left(p), l, mid);
            build(right(p), mid + 1, r);
            int m = Math.min(o[left(p)], c[right(p)]);
            t[p] = t[left(p)] + t[right(p)] + m;
            o[p] = o[left(p)] + o[right(p)] - m;
            c[p] = c[left(p)] + c[right(p)] - m;
        }

        serejaAndBrackets.node query(int p, int l, int r, int i, int j) {
            if (i > r || j < l) {
                return new serejaAndBrackets.node(0, 0, 0);
            }
            if (l >= i && r <= j) {
                return new serejaAndBrackets.node(t[p], o[p], c[p]);
            }
            int mid = (l + r) / 2;
            serejaAndBrackets.node n1 = query(left(p), l, mid, i, j);
            serejaAndBrackets.node n2 = query(right(p), mid + 1, r, i, j);

            int tmp = Math.min(n1.o, n2.c);
            int t = n1.t + n2.t + tmp;
            int o = n1.o + n2.o - tmp;
            int c = n1.c + n2.c - tmp;

            return new serejaAndBrackets.node(t, o, c);

        }

        int right(int p) {
            return (p << 1) + 1;
        }

        int left(int p) {
            return p << 1;
        }

        static class node {
            int t;
            int o;
            int c;

            public node(int t, int o, int c) {
                this.t = t;
                this.o = o;
                this.c = c;
            }

        }

    }

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

    }

    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 String next() {
            return nextString();
        }

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

        }

    }
}

