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.InputStreamReader;
import java.util.StringTokenizer;


public class E2 {
    static seg tree[];
     static int left(int i){return i*2;}
     static int right(int i){return (i*2)+1;}
     static int mid(int l,int h){return (l+h)/2;}
    static char a[];
    static StringBuilder b=new StringBuilder();
    public static void main(String[] args) throws Exception{
        a=str().toCharArray();
        tree=new seg[4*a.length];
        build(1,0,a.length-1);
        int m=in();
        for (int i=0;i<m;i++){
            b.append(quar(1, 0, a.length-1,in()-1, in()-1).bal+"\n");
        }
        System.out.print(b);
    }
    private static seg build(int i, int l, int h) {
        if (l==h){
            if (a[l]=='(')return tree[i]= new seg(0,1,0);
            else return tree[i] =new seg(0,0,1);
        }
        seg lef=build(left(i), l, mid(l,h));
        seg ri=build(right(i),mid(l, h)+1 , h);
        return tree[i]=merge(lef, ri);
    }
    private static seg merge(seg lef, seg ri) {
        int res=lef.bal+ri.bal+Math.min(lef.open, ri.close)*2;
        int o=lef.open-Math.min(lef.open, ri.close)+ri.open;
        int c=ri.close-Math.min(lef.open, ri.close)+lef.close;
        return new seg(res, o, c);
    }
    static seg quar(int i,int l,int h,int l1,int h1){
            if (l>=l1 && h<=h1){
                return tree[i];
            }
            if (h<l1 || l>h1)return null;
            seg lef=quar(left(i), l, mid(l,h),l1,h1);
            seg ri=quar(right(i),mid(l, h)+1 , h,l1,h1);
            if (lef==null)return ri;
            if (ri==null)return lef;
            return merge(lef, ri);
    }
    static BufferedReader buf=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static int in() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return Integer.parseInt(st.nextToken());
    }
    static long ll() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return Long.parseLong(st.nextToken());
    }
    static String str() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return (st.nextToken());
    }
        static double dub() throws IOException{
            if (st==null || !st.hasMoreTokens()){
                st=new StringTokenizer(buf.readLine());
            }
            return Double.parseDouble(st.nextToken());
    }

}
class seg{
    int open;
    int close;
    int bal;
    seg(int b,int o,int c){
        open =o;
        bal=b;
        close=c;
    }
}