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 SegmentTree;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class BracketSequence {
    public static Sequence query(Sequence tree[],int s,int e,int l,int r,int node){
        if(s>r||e<l){
            return new Sequence();
        }
        if(s>=l&&e<=r){
            return tree[node];
        }
        int mid=(s+e)/2;
        Sequence left=query(tree,s,mid,l,r,2*node);
        Sequence right=query(tree,mid+1,e,l,r,2*node+1);
        Sequence ans=new Sequence();
        ans.val=left.val+right.val;
        int x=Math.min(left.b,right.c);
        ans.val+=2*x;
        ans.b=left.b+right.b-x;
        ans.c=left.c+right.c-x;
        return ans;
    }
    public static void build(Sequence tree[],String str,int s,int e,int node){
        if(s==e){
            char c=str.charAt(s-1);
            tree[node]=new Sequence();
            if(c=='('){
                tree[node].b=1;
            }
            else{
                tree[node].c=1;
            }
            return;
        }
        int mid=(s+e)/2;
        build(tree,str,s,mid,2*node);
        build(tree,str,mid+1,e,2*node+1);
        tree[node]=new Sequence();
        Sequence left=tree[2*node];
        Sequence right=tree[2*node+1];
        tree[node].val=left.val+right.val;
        int x=Math.min(left.b,right.c);
        tree[node].val+=2*x;
        tree[node].b=left.b+right.b-x;
        tree[node].c=left.c+right.c-x;
    }
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String str=br.readLine();
        StringTokenizer st;
        int n=str.length();
        Sequence tree[]=new Sequence[4*n+4];
        build(tree,str,1,n,1);
        int q=Integer.parseInt(br.readLine());
        StringBuilder print=new StringBuilder();
        while(q--!=0){
            st=new StringTokenizer(br.readLine());
            int l=Integer.parseInt(st.nextToken());
            int r=Integer.parseInt(st.nextToken());
            Sequence ans=query(tree,1,n,l,r,1);
//            System.out.println(ans);
            print.append(ans.val+"\n");
        }
        System.out.print(print.toString());
    }
}

class Sequence{
    int val,b,c;
    public Sequence(){
        this.val=0;
        this.b=0;
        this.c=0;
    }

    @Override
    public String toString() {
        return this.val+" "+this.b+" "+this.c;
    }
}
