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.math.*;
import java.io.*;
import java.util.*;

public class Main {
    
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    
}

class Node {
    
    int open, close;
    int length;
    
    Node() {
        open = 0;
        close = 0;
        length = 0;
    }
    
    Node(int open, int close, int length) {
        this.open = open;
        this.close = close;
        this.length = length;
    }
    
    Node(Node left, Node right) {
        this.length = left.length + right.length + 2 * Math.min(left.open, right.close);
        this.open = right.open + left.open - Math.min(left.open, right.close);
        this.close = left.close + right.close - Math.min(left.open, right.close);
    }
}

class Task {
    
    Node[] t;
    char[] s;
    int n;
    
    void build(int v, int l, int r) {
        if(l == r) {
            t[v] = new Node(s[l] == '(' ? 1 : 0, s[l] == ')' ? 1 : 0, 0);
            return;
        }
        int mid = (l + r) / 2;
        build(2 * v + 1, l, mid);
        build(2 * v + 2, mid + 1, r);
        t[v] = new Node(t[2 * v + 1], t[2 * v + 2]);
    }
    
    Node query(int v, int tl, int tr, int l, int r) {
        if(tl == l && r == tr) {
            return t[v];
        }
        int tm = (tl + tr) / 2;
        if(r <= tm) {
            return query(2 * v + 1, tl, tm, l, r);
        }
        if(l > tm) {
            return query(2 * v + 2, tm + 1, tr, l, r);
        }
        return new Node(query(2 * v + 1, tl, tm, l, tm),
                query(2 * v + 2, tm + 1, tr, tm + 1, r));
    }
    
    public void solve(FastReader in, PrintWriter out) throws IOException {
       s = in.next().toCharArray();
       n = s.length;
       t = new Node[4 * n];
       build(0, 0, n - 1);
       int q = in.nextInt();
       while(q --> 0) {
           int l = in.nextInt(), r = in.nextInt();
           out.println(query(0, 0, n - 1, l - 1, r - 1).length);
       }
    }
    
}

class FastReader {
    
    BufferedReader in;
    StringBuilder sb = new StringBuilder();
    
    public FastReader(BufferedReader in) {
        this.in = in;
    }
    
    public String next() throws IOException {
        sb.setLength(0);
        while(true) {
            int c = in.read();
            if(c == -1) {
                return null;
            }
            if(" \n\r\t".indexOf(c) == -1) {
                sb.append((char)c);
                break;
            }
        }
        while(true) {
            int c = in.read();
            if(c == -1 || " \n\r\t".indexOf(c) != -1) {
                break;
            }
            sb.append((char)c);
        }
        return sb.toString();
    }
    
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    
}
