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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * 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);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    int N = (int) 1e6;
    NODE[] tree = new NODE[N * 4];

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        String s = in.next();
        buildTree(s, 1, 0, s.length() - 1);
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int l = in.nextInt() - 1, r = in.nextInt() - 1;
            out.println(solveTree(1, 0, s.length() - 1, l, r).size * 2);
        }
    }

    public void buildTree(String s, int p, int l, int r) {
        if (l == r) {
            tree[p] = new NODE();
            tree[p].size = 0;
            tree[p].l = s.charAt(l) == '(' ? 1 : 0;
            tree[p].r = s.charAt(l) == ')' ? 1 : 0;
            return;
        }

        int m = (l + r) / 2;

        buildTree(s, p * 2, l, m);
        buildTree(s, p * 2 + 1, m + 1, r);

        tree[p] = merge(tree[p * 2], tree[p * 2 + 1]);
    }

    public NODE solveTree(int p, int l, int r, int ll, int rr) {
        if (ll > rr) {
            return new NODE();
        }

        if (l == ll && r == rr) {
            NODE node = new NODE();
            node.l = tree[p].l;
            node.r = tree[p].r;
            node.size = tree[p].size;
            return node;
        }

        int m = (l + r) / 2;
        return merge(solveTree(p * 2, l, m, ll, Math.min(m, rr)),
                solveTree(p * 2 + 1, m + 1, r, Math.max(m + 1, ll), rr));
    }

    public NODE merge(NODE a, NODE b) {
        NODE n = new NODE();
        int d = Math.min(a.l, b.r);
        n.size = a.size + b.size + d;
        n.l = a.l + b.l - d;
        n.r = a.r + b.r - d;
        return n;
    }

    public static class NODE {
        int size;
        int l, r;
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

}

