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.util.*;

public class Main {
    class Node {
        int l, r, tot;

        Node(int _l, int _r, int _tot) {
            l = _l;
            r = _r;
            tot = _tot;
        }
    }

    Node node[];
    String s;

    Node Up(Node ls, Node rs) {
        Node fa = new Node(0, 0, 0);
        int v = Math.min(ls.l, rs.r);
        fa.tot = v + ls.tot + rs.tot;
        fa.l = ls.l + rs.l - v;
        fa.r = ls.r + rs.r - v;
        return fa;
    }

    Node query(int L, int R, int l, int r, int rt) {
        if (L <= l && r <= R)
            return node[rt];
        int mid = (l + r) >> 1;
        if (R <= mid)
            return query(L, R, l, mid, rt << 1);
        else if (L > mid)
            return query(L, R, mid + 1, r, rt << 1 | 1);
        else {
            Node ls = query(L, mid, l, mid, rt << 1), rs = query(mid + 1, R,
                    mid + 1, r, rt << 1 | 1);
            Node re = Up(ls, rs);
            return re;
        }
    }

    void build(int l, int r, int rt) {
        node[rt] = new Node(0, 0, 0);
        if (l == r) {
            if (s.charAt(l) == '(')
                ++node[rt].l;
            else
                ++node[rt].r;
            return;
        }
        int mid = (l + r) >> 1;
        build(l, mid, rt << 1);
        build(mid + 1, r, rt << 1 | 1);
        node[rt] = Up(node[rt << 1], node[rt << 1 | 1]);
    }

    void run() throws IOException {
        s = cin.next();
        int n = s.length();
        node = new Node[n << 2];

        build(0, n - 1, 1);
        int q = cin.nextInt(), l, r;
        while (q-- > 0) {
            l = cin.nextInt() - 1;
            r = cin.nextInt() - 1;
            out.println(2 * query(l, r, 0, n - 1, 1).tot);
        }
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    Main() {
        cin = new InputReader(System.in);
        // cin = new Scanner(System.in);
        out = new PrintWriter(System.out);
    }

    PrintWriter out;
    InputReader cin;

    // Scanner cin;

    class InputReader {
        InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            // try {
            // reader = new BufferedReader(new FileReader("input.txt"));
            // } catch (FileNotFoundException ex) {
            // }
            tokenizer = new StringTokenizer("");
        }

        private String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        private BufferedReader reader;
        private StringTokenizer tokenizer;
    }
}