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.StringTokenizer;

public class Contest380C {
    public static PrintWriter out = new PrintWriter(System.out);
    public static FastScanner enter = new FastScanner(System.in);

    public static void main(String[] args) throws IOException {
        String s=enter.next();
        SegmentTree segmentTree=new SegmentTree(s.length(),s);
        segmentTree.build(1,0,s.length()-1);
        int k=enter.nextInt();
        for (int i = 0; i <k ; i++) {
            int l=enter.nextInt();
            int r=enter.nextInt();
            tuple ans=segmentTree.query(1,0,s.length()-1,l-1,r-1);
            out.println(ans.len);
        }
        out.close();
    }

    static class SegmentTree{
        tuple[] t;
        String s;
        public SegmentTree(int nElements, String s) {
            t=new tuple[nElements*4+1];
            this.s=s;
        }

        public void build(int v, int vl, int vr){
            if(vl==vr){
                t[v]=new tuple(0, (s.charAt(vl)=='(')? 1:0, (s.charAt(vl)=='(')? 0:1);
                return;
            }
            int tmp=(vl+vr)/2;
            build(2*v, vl, tmp);
            build(2*v+1, tmp+1, vr);
            int tt=Math.min(t[2*v].open, t[2*v+1].close);
            t[v]=new tuple(t[2*v].len+t[2*v+1].len+2*tt, t[2*v].open+t[2*v+1].open-tt, t[2*v].close+t[2*v+1].close-tt);
        }
        public tuple query(int v, int vl, int vr, int l, int r){
            if(l>r){
                return new tuple(0,0,0);
            }
            if(vl==l && vr ==r) return t[v];
            int tmp=(vl+vr)/2;
            tuple t1=query(2*v, vl, tmp, l , Math.min(r, tmp));
            tuple t2=query(2*v+1, tmp+1, vr, Math.max(l,tmp+1), r);
            int tt=Math.min(t1.open, t2.close);
            return new tuple(t1.len+t2.len+2*tt, t1.open+t2.open-tt, t1.close+t2.close-tt);
        }
    }

    static class tuple{
        int len;
        int open;
        int close;

        public tuple(int len, int open, int close) {
            this.len = len;
            this.open = open;
            this.close = close;
        }
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer stok;

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        String next() throws IOException {
            while (stok == null || !stok.hasMoreTokens()) {
                String s = br.readLine();
                if (s == null) {
                    return null;
                }
                stok = new StringTokenizer(s);
            }
            return stok.nextToken();
        }

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

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        char nextChar() throws IOException {
            return (char) (br.read());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }
    }
}
