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.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String... args) {
        MyScanner in = new MyScanner(System.in);

        char[] inputs = in.next().toCharArray();
        int inputsLength = inputs.length;
        int fullLength = Integer.highestOneBit(inputsLength) * 4;
        int halfLength = fullLength / 2;

//        System.out.println(fullLength);

        int[] lOpened = new int[fullLength];
        int[] rOpened = new int[fullLength];
        int[] pairs = new int[fullLength];

        for (int i = 0; i < inputsLength; i++) {
            if (inputs[i] == '(') {
                lOpened[halfLength + i] = 1;
            } else {
                rOpened[halfLength + i] = 1;
            }
        }

        for (int i = halfLength - 1; i >= 1; i--) {
            int newPairs = Math.min(lOpened[i * 2], rOpened[i * 2 + 1]);

            pairs[i] = newPairs + pairs[i * 2] + pairs[i * 2 + 1];
            lOpened[i] = lOpened[i * 2] + lOpened[i * 2 + 1] - newPairs;
            rOpened[i] = rOpened[i * 2] + rOpened[i * 2 + 1] - newPairs;
        }

//        System.out.println(Arrays.toString(inputs));
//        System.out.println(Arrays.toString(pairs));
//        System.out.println(Arrays.toString(lOpened));
//        System.out.println(Arrays.toString(rOpened));

        int queryCount = in.nextInt();
        for (int i = 0; i < queryCount; i++) {
            System.out.println(calc(lOpened, rOpened, pairs, in.nextInt(), in.nextInt(), halfLength) * 2);
        }
    }

    public static long calc(int[] lOpened, int[] rOpened, int[] pairs, int l, int r, int halfLength) {
        l += halfLength - 1;
        r += halfLength - 1;

        int lOpeneds = 0;
        int lPairs = 0;
        int rOpeneds = 0;
        int rPairs = 0;

        while (l <= r) {
            if ((l & 1) == 1) {
                lPairs += Math.min(lOpeneds, rOpened[l]) + pairs[l];
                lOpeneds += lOpened[l] - Math.min(lOpeneds, rOpened[l]);

                l++;
            }
            l >>= 1;

            if ((r & 1) == 0) {
                rPairs += Math.min(rOpeneds, lOpened[r]) + pairs[r];
                rOpeneds += rOpened[r] - Math.min(rOpeneds, lOpened[r]);

                r--;
            }
            r >>= 1;
        }

        return lPairs + rPairs + Math.min(lOpeneds, rOpeneds);
    }

    public static class MyScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public MyScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return tokenizer.nextToken();
        }

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

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