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 «()(())(())».
//package codeforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class E {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    @SuppressWarnings("unchecked")
    void solve() throws IOException {
        char[] s = next().toCharArray();
        final int n = s.length;
        int[] sum = new int[n + 1];
        for(int i = 1; i <= n; i++) {
            sum[i] = sum[i - 1] + (s[i - 1] == '(' ? 1 : -1);
        }
        class SegmentTree {
            int q = 1;
            int[] a;
            {
                while(q <= n) q *= 2;
                a = new int[2 * q];
                Arrays.fill(a, Integer.MAX_VALUE);
            }

            void update(int i, int x) {
                for(i += q; i > 0; i /= 2) {
                    a[i] = Math.min(a[i], x);
                }
            }

            int min(int l, int r) {
                int result = Integer.MAX_VALUE;
                for(l += q, r += q; l < r; l /= 2, r /= 2) {
                    if(l % 2 == 1) {
                        result = Math.min(result, a[l++]);
                    }
                    if(r % 2 == 1) {
                        result = Math.min(result, a[--r]);
                    }
                }
                return result;
            }
        }
        SegmentTree segmentTree = new SegmentTree();
        for(int i = 0; i <= n; i++) {
            segmentTree.update(i, sum[i]);
        }
        for(int q = nextInt(); q > 0; q--) {
            int l = nextInt(), r = nextInt();
            int base = sum[l - 1];
            int min = segmentTree.min(l, r + 1) - base;
            //open + closed = r - l + 1
            //open - closed = sum[r] - sum[l - 1]
            int closed = (r - l + 1 - sum[r] + sum[l - 1]) / 2;
            if(min < 0) closed += min;
            writer.println(Math.max(0, closed * 2));
        }
        writer.close();
    }

    public static void main(String[] args) throws IOException {
        new E().solve();
    }
}


