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.*;
import java.nio.charset.StandardCharsets;

public class SerejaAndBrackets380 {

    private static int nextInt(StreamTokenizer t) throws IOException {
        t.nextToken();
        return (int) t.nval;
    }

    public static class SegnemtTreeRMQ {
        private int[] t;
        private final int n;

        SegnemtTreeRMQ(int n) {
            this.n = n;
            this.t = new int[2 * n];
        }

        void add(int i, int value) {
            int pos = i + n;
            t[pos] = value;
            update(pos / 2);
        }

        void update(int parent) {
            if (parent >= 1) {
                t[parent] = Math.min(t[2 * parent], t[2 * parent + 1]);
                update(parent / 2);
            }
        }

        int min(int l, int r) {
            return minr(l + n, r + n);
        }

        int minr(int l, int r) {
            if (l > r) {
                return Integer.MAX_VALUE;
            }

            return Math.min(t[l], Math.min(t[r], minr((l + 1) / 2, (r - 1) / 2)));
        }
    }

    public static void main(String[] args) throws IOException {
        try (final BufferedReader in = new BufferedReader(new InputStreamReader(System.in, StandardCharsets.UTF_8));
             final PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out, StandardCharsets.UTF_8))) {
            final StreamTokenizer t = new StreamTokenizer(in);

            char[] b = in.readLine().toCharArray();
            int n = b.length;

            SegnemtTreeRMQ rmq = new SegnemtTreeRMQ(n + 1);
            int[] h = new int[n + 1];
            int height = 0;
            for (int i = 0; i < n; i++) {
                if (b[i] == '(') {
                    height++;
                } else {
                    height--;
                }
                h[i + 1] = height;
                rmq.add(i + 1, height);
            }

            int m = nextInt(t);
            for (int i = 0; i < m; i++) {
                int l = nextInt(t);
                int r = nextInt(t);
                int min = rmq.min(l - 1, r);
                int left = h[l - 1] - min;
                int right = h[r] - min;
                out.write(r - l + 1 - left - right + "\n");
            }

            out.flush();
        }
    }
}
