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
 */
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 {
        Node nothing = new Node(0, 0, 0, 0, 0);
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            char[] s = in.next().toCharArray();
            ST st = new ST(s);
            int numQueries = in.readInt();
            for (int query = 0; query < numQueries; query++) {
                out.printLine(st.query(in.readInt() - 1, in.readInt() - 1));
            }
        }
        class Node {
            Node l;
            Node r;
            int left;
            int right;
            int work;
            int freeLeft;
            int freeRight;
            public Node(int left, int right, int work, int freeLeft, int freeRight) {
                this.left = left;
                this.right = right;
                this.work = work;
                this.freeLeft = freeLeft;
                this.freeRight = freeRight;
            }
        }
        class ST {
            char[] s;
            Node root;
            Node init(int left, int right) {
                if (left == right) {
                    if (s[left] == '(') return new Node(left, right, 0, 1, 0);
                    else return new Node(left, right, 0, 0, 1);
                }
                int mid = (left + right) / 2;
                Node l = init(left, mid);
                Node r = init(mid + 1, right);
                int nWork = l.work + r.work;
                int nLeft = l.freeLeft + r.freeLeft;
                int nRight = r.freeRight + l.freeRight;
                if (l.freeLeft > 0 && r.freeRight > 0) {
                    int cancombine = Math.min(l.freeLeft, r.freeRight);
                    nWork += cancombine * 2;
                    nLeft -= cancombine;
                    nRight -= cancombine;
                }
                Node res = new Node(left, right, nWork, nLeft, nRight);
                res.l = l;
                res.r = r;
                return res;
            }
            public ST(char[] s) {
                this.s = s;
                root = init(0, s.length - 1);
            }
            Node query(Node cur, int left, int right) {
                if (right < cur.left) return nothing;
                if (left > cur.right) return nothing;
                if (left <= cur.left && cur.right <= right) return cur;
                Node l = query(cur.l, left, right);
                Node r = query(cur.r, left, right);
                int nWork = l.work + r.work;
                int nLeft = l.freeLeft + r.freeLeft;
                int nRight = r.freeRight + l.freeRight;
                if (l.freeLeft > 0 && r.freeRight > 0) {
                    int cancombine = Math.min(l.freeLeft, r.freeRight);
                    nWork += cancombine * 2;
                    nLeft -= cancombine;
                    nRight -= cancombine;
                }
                return new Node(left, right, nWork, nLeft, nRight);
            }
            int query(int left, int right) {
                return query(root, left, right).work;
            }
        }
    }
    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);
        }
    }
}

