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.*;
import java.util.*;
public class jkl{

    static int seg[];
    public static void main(String args[]){
        Scan sc=new Scan(System.in);
        char ch[]=sc.next().toCharArray();
        int n=ch.length;
        int dp[]=new int[n+1];
        seg=new int[4*n+1];
        for(int i=0;i<n;i++){
            dp[i+1]=dp[i];
            if(ch[i]=='(')
                dp[i+1]++;
            else
                dp[i+1]--;

        }
       // for(int i:dp)
           // System.out.print(i+" ");
       // System.out.println(query(0,n-1,));

build(0,n,0,dp);

StringBuilder sb=new StringBuilder();

        int m=sc.nextInt();
        while(m-->0){
        int x=sc.nextInt();
        int y=sc.nextInt();
        int ans=y-x+1;
        int temp=query(0,n,x,y,0);
        temp-=dp[x-1];
        int temp1=dp[y]-dp[x-1];
        if(temp<0)
        {ans+=temp;
        temp1-=temp;
        }
        if(temp1>0){
            ans-=temp1;
        }

           sb.append(ans+"\n");
        }
        System.out.println(sb.toString());
    }

    public static void build(int l,int r,int pos,int arr[]){
        if(l==r)
        {seg[pos]=arr[l];return;}

        int m=(l+r)/2;
        build(l,m,2*pos+1,arr);
        build(m+1,r,2*pos+2,arr);
        seg[pos]=Math.min(seg[2*pos+1],seg[2*pos+2]);
    }
    public static int query(int l,int r,int ql,int qr,int pos){
        if(ql>r || qr<l)
            return Integer.MAX_VALUE;
        if(ql<=l && qr>=r)
            return seg[pos];
        int m=(l+r)/2;
        return Math.min(query(l,m,ql,qr,2*pos+1),query(m+1,r,ql,qr,2*pos+2));

    }

    static class Scan {
        StringTokenizer st;
        BufferedReader br;

        public Scan(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
                ;
            }
            return st.nextToken();
        }

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

    }
}



