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 SerejaBrackets {
    void solve() {
        char[] s = in.nextToken().toCharArray();
        
        int m = in.nextInt();
        SegmentTree seg = new SegmentTree(s);
        for (int i = 0; i < m; i++) {
            int l = in.nextInt() - 1, r = in.nextInt();
            int[] ret = seg.query(l, r);
            out.println(ret[0] << 1);
        }
    }
    
    static class SegmentTree {
        int n;
        int[] a, b, c;
        
        SegmentTree(char[] s) {
            n = Integer.highestOneBit(s.length) << 1;
            a = new int[2 * n - 1];
            b = new int[2 * n - 1];
            c = new int[2 * n - 1];
            
            for (int i = 0; i < s.length; i++) {
                a[n - 1 + i] = 0;
                if (s[i] == '(') b[n - 1 + i]++;
                else c[n - 1 + i]++;
            }
            for (int i = n - 2; i >= 0; i--) {
                int t = Math.min(b[2 * i + 1], c[2 * i + 2]);
                a[i] = a[2 * i + 1] + a[2 * i + 2] + t;
                b[i] = b[2 * i + 1] + b[2 * i + 2] - t;
                c[i] = c[2 * i + 1] + c[2 * i + 2] - t;
            }
        }
        
        int[] query(int a, int b) {
            return query(a, b, 0, 0, n);
        }
        
        int[] query(int a, int b, int k, int l, int r) {
            if (a >= r || b <= l) return new int[]{0, 0, 0};
            if (a <= l && r <= b) return new int[]{this.a[k], this.b[k], this.c[k]};
            int[] r1 = query(a, b, 2 * k + 1, l, (l + r) / 2);
            int[] r2 = query(a, b, 2 * k + 2, (l + r) / 2, r);
            int t = Math.min(r1[1], r2[2]);
            int na = r1[0] + r2[0] + t;
            int nb = r1[1] + r2[1] - t;
            int nc = r1[2] + r2[2] - t;
            return new int[]{na, nb, nc};
        }
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new SerejaBrackets().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());
        }
    }
}
