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.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution {
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
    static class TreeNode
    {
        int left, right, open, close, answer;
        
        public TreeNode(int a, int b, int c, int d, int e)
        {
            left = a;
            right = b;
            open = c;
            close = d;
            answer = e;
        }
    }
    
    static TreeNode[] tree;
    
    static char[] arr;
    
    public static TreeNode buildTree(int index, int i, int j)
    {
        int open = 0, close = 0;
        
        if(i == j)
        {
            if(arr[i] == '(')
            {
                open = 1;
            }
            else
            {
                close = 1;
            }
            
            return tree[index] = new TreeNode(i, j, open, close, 0);
        }
        
        TreeNode leftChild = buildTree(2*index + 1, i, (i + j) >> 1);
        TreeNode rightChild = buildTree(2*index + 2, ((i + j) >> 1) + 1, j);
        
        int minCompatible = Math.min(leftChild.open, rightChild.close);
        
        int answer = leftChild.answer + rightChild.answer + 2*minCompatible;
        
        int remainOpen = rightChild.open + leftChild.open - minCompatible;
        int remainClose = leftChild.close + rightChild.close - minCompatible;
        
        return tree[index] = new TreeNode(i, j, remainOpen, remainClose, answer);
        
    }
    
    public static TreeNode answerQuery(int index, int i, int j)
    {
        if(tree[index].left >= i && tree[index].right <= j)
            return tree[index];
        
        if(tree[index].right < i || tree[index].left > j)
                return new TreeNode(0,0,0,0,0);
        
        TreeNode leftChild = answerQuery(2*index + 1, i, j);
        TreeNode rightChild = answerQuery(2*index + 2, i, j);
        
        int minCompatible = Math.min(leftChild.open, rightChild.close);
        
        int answer = leftChild.answer + rightChild.answer + 2*minCompatible;
        
        int remainOpen = rightChild.open + leftChild.open - minCompatible;
        int remainClose = leftChild.close + rightChild.close - minCompatible;
        
        return new TreeNode(i, j, remainOpen, remainClose, answer);
    }
    
    public static void main(String[] args) {
        
        InputReader in = new InputReader(System.in);
        
        arr = in.next().toCharArray();
        tree = new TreeNode[4*arr.length];
        
        buildTree(0, 0, arr.length - 1);
        
        int q = in.nextInt();
        
        PrintWriter out = new PrintWriter(System.out);
        for(int i = 0; i < q; i++)
        {
            int x, y;
            x = in.nextInt() - 1;
            y = in.nextInt() - 1;
            
            out.println(answerQuery(0, x, y).answer);
        }
        
        out.flush();
    }
}
