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

/**
 * @author Don Li
 */
public class SerejaBrackets2 {
    
    int n;
    Node[] t;
    
    void solve() {
        char[] s = in.nextToken().toCharArray();

        n = s.length;
        t = new Node[n << 1];
        for (int i = 0; i < n; i++) {
            t[n + i] = new Node(0, s[i] == '(' ? 1 : 0, s[i] == ')' ? 1 : 0);
        }
        for (int i = n - 1; i > 0; i--) {
            t[i] = combine(t[i << 1], t[i << 1 | 1]);
        }
        
        int q = in.nextInt();
        for (int i = 0; i < q; i++) {
            int l = in.nextInt() - 1, r = in.nextInt();
            Node res = query(l, r);
            out.println(res.pair << 1);
        }
    }
    
    Node query(int l, int r) {
        Node L = new Node(), R = new Node();
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if ((l & 1) > 0) L = combine(L, t[l++]);
            if ((r & 1) > 0) R = combine(t[--r], R);
        }
        return combine(L, R);
    }
    
    Node combine(Node a, Node b) {
        int cnt = Math.min(a.open, b.close);
        return new Node(a.pair + b.pair + cnt, a.open + b.open - cnt, a.close + b.close - cnt);
    }
    
    static class Node {
        int pair, open, close;
        
        public Node() {
        }
        
        public Node(int pair, int open, int close) {
            this.pair = pair;
            this.open = open;
            this.close = close;
        }
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new SerejaBrackets2().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
