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 sumit
 */
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 {
            Pair2[] seg;

            void build(Pair2[] arr) {
                  int n = arr.length;
                  seg = new Pair2[2 * n];
                  for (int i = 0; i < n; i++) {
                        seg[i + n] = new Pair2(arr[i].ans, arr[i].close, arr[i].open);
                  }
                  for (int i = n - 1; i > 0; i--) {
                        int ch1 = i << 1;
                        int ch2 = (i << 1) + 1;

                        int zz = Math.min(seg[ch1].open, seg[ch2].close);
                        seg[i] = new Pair2(0, 0, 0);
                        seg[i].ans = seg[ch1].ans + seg[ch2].ans + zz;
                        seg[i].open = seg[ch1].open + seg[ch2].open - zz;
                        seg[i].close = seg[ch1].close + seg[ch2].close - zz;
                  }
            }

            Pair2 add(Pair2 a1, Pair2 a2) {
                  int zz = Math.min(a1.open, a2.close);
                  Pair2 ans = new Pair2(0, 0, 0);
                  ans.ans = a1.ans + a2.ans + zz;
                  ans.open = a1.open + a2.open - zz;
                  ans.close = a1.close + a2.close - zz;
                  return ans;
            }

            int query(int l, int r, int n) {
                  Pair2 ans1 = new Pair2(0, 0, 0);
                  Pair2 ans2 = new Pair2(0, 0, 0);
                  for (int i = l + n, j = r + n; i <= j; i = (i >> 1), j = (j >> 1)) {
                        if ((i & 1) == 1) {
                              ans1 = add(ans1, seg[i]);
                              i++;
                        }
                        if ((j & 1) == 0) {
                              ans2 = add(seg[j], ans2);
                              j--;
                        }
                  }
                  return add(ans1, ans2).ans;
            }

            public void solve(int testNumber, InputReader in, OutputWriter out) {
                  String str = in.next();
                  Pair2[] arr = new Pair2[str.length()];
                  for (int i = 0; i < str.length(); i++) {
                        if (str.charAt(i) == ')') {
                              arr[i] = new Pair2(0, 1, 0);
                        } else {
                              arr[i] = new Pair2(0, 0, 1);
                        }
                  }
                  build(arr);
                  ;
                  int q = in.nextInt();
                  StringBuilder ss = new StringBuilder();
                  while (q-- > 0) {
                        int l = in.nextInt();
                        int r = in.nextInt();

                        ss.append(2 * query(l - 1, r - 1, str.length()));
                        ss.append("\n");
                  }
                  out.printLine(ss.toString());

            }

            class Pair2 {
                  int ans;
                  int close;
                  int open;

                  Pair2(int ans, int close, int open) {
                        this.close = close;
                        this.open = open;
                        this.ans = ans;
                  }

            }

      }

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

            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 & 15;

                        c = read();
                  } while (!isSpaceChar(c));

                  return res * sgn;
            }

            public String next() {
                  int c = read();

                  while (isSpaceChar(c))
                        c = read();

                  StringBuilder res = new StringBuilder();

                  do {
                        res.appendCodePoint(c);

                        c = read();
                  } while (!isSpaceChar(c));

                  return res.toString();
            }

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

      }

      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 print(Object... objects) {
                  for (int i = 0; i < objects.length; i++) {
                        if (i != 0) {
                              writer.print(' ');
                        }
                        writer.print(objects[i]);
                  }
            }

            public void printLine(Object... objects) {
                  print(objects);
                  writer.println();
            }

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

      }
}

