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 NickMikeMurderers;

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

public class SerejaAndBrackets {
    public static void build(int tree[],int a[],int s,int e,int node){
        if(s==e){
            tree[node]=a[s];
            return;
        }
        int mid=(s+e)>>1;
        build(tree,a,s,mid,2*node);
        build(tree,a,mid+1,e,2*node+1);
        tree[node]=Math.min(tree[2*node],tree[2*node+1]);
    }
    public static int query(int tree[],int s,int e,int l,int r,int node){
        if(s>r||e<l){
            return Integer.MAX_VALUE;
        }
        if(l<=s&&r>=e){
            return tree[node];
        }
        int mid=(s+e)>>1;
        int ans1=query(tree,s,mid,l,r,2*node);
        int ans2=query(tree,mid+1,e,l,r,2*node+1);
        return Math.min(ans1,ans2);
    }
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        char str[]=br.readLine().toCharArray();
        int q=Integer.parseInt(br.readLine());
        int n=str.length;
        StringBuilder print=new StringBuilder();
        int presum[]=new int[n+1];
        int back[]=new int[n+1];
        for(int i=1;i<=n;i++){
            char c=str[i-1];
            if(c=='('){
                presum[i]=presum[i-1]+1;
                back[i]=back[i-1];
            }
            else{
                presum[i]=presum[i-1]-1;
                back[i]=back[i-1]+1;
            }
        }
        int tree[]=new int[4*n+4];
        build(tree,presum,0,n,1);
        while(q--!=0){
            StringTokenizer st=new StringTokenizer(br.readLine());
            int l=Integer.parseInt(st.nextToken());
            int r=Integer.parseInt(st.nextToken());
            int total_back=back[r]-back[l-1];
            int red=presum[l-1];
            red-=query(tree,0,n,l-1,r,1);
            total_back-=red;
            total_back*=2;
            print.append(total_back).append("\n");
        }
        System.out.print(print.toString());
    }
}
