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.util.Scanner;

public class SerejaAndBrackets {

    static Node buid(Node tree,String s,int i,int j){
        if(tree == null)
            tree = new Node();
        tree.leftIndex = i;
        tree.rightIndex = j;
        if( i == j){
            tree.value = 0;
            if(s.charAt(i)=='(')
                tree.left_b++;
            else
                tree.right_b++;
            return tree;
        }
        tree.left = buid(tree.left,s,i,i+(j-i)/2);
        tree.right = buid(tree.right,s,i+(j-i)/2+1,j);

        tree.value = tree.left.value + tree.right.value + min(tree.left.left_b,tree.right.right_b);
        tree.left_b = tree.left.left_b + tree.right.left_b - min(tree.left.left_b,tree.right.right_b);
        tree.right_b = tree.left.right_b + tree.right.right_b - min(tree.left.left_b,tree.right.right_b);

        return tree;
    }

    static Node query(Node tree,String s,int i,int j){
        if(tree.leftIndex > j || tree.rightIndex < i){
            return null;
        }

        if(tree.leftIndex >= i && tree.rightIndex <= j){
            return tree;
        }


        Node p = query(tree.left,s,i,j);
        Node q = query(tree.right,s,i,j);

        if(p == null){
            return q;
        }

        if(q == null){
            return p;
        }

        Node node = new Node();
        node.value = p.value + q.value + min(p.left_b,q.right_b);
        node.left_b = p.left_b + q.left_b - min(p.left_b,q.right_b);
        node.right_b = p.right_b + q.right_b - min(p.left_b,q.right_b);
        return node;
    }

    static int min(int a, int b){
        if(a<b)
            return a;
        return b;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String sequence = sc.next();
        Node tree = new Node();
        tree = buid(tree,sequence,0,sequence.length()-1);
        int n = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for(int i =0; i <n;i++){
            int x = sc.nextInt();
            int y = sc.nextInt();
            sb.append(2*query(tree,sequence,x-1,y-1).value);
            sb.append("\n");
        }
        System.out.println(sb.toString());
    }
}
class Node{
    int left_b,right_b,value;
    int leftIndex,rightIndex;
    Node left, right;
}