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.*;
import java.io.*;
import static java.lang.Math.*;
public class Main {
    static final long MOD = 1_000_000_007, INF = 1_000_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //variables here
    static String s;
    static int n;
    static Pair tree[];
    static void magic() {
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        s = reader.next();
        n = s.length();
        int sz = (int)(pow(2, ceil(log(n)/log(2))+1));
        tree = new Pair[sz];
        build(1,0,n-1);
        int q = reader.nextInt();
        StringBuilder fast = new StringBuilder();
        while(q-->0) {
            int l = reader.nextInt()-1, r = reader.nextInt()-1;
            Pair p = query(l,r);
            int ans = (r-l+1) - p.nOpenBrackets - p.nCloseBrackets;
            fast.append(ans);
            fast.append("\n");
        }
        writer.println(fast);
    }
    static void build(int treein, int low, int high) {
        if(low==high) {
            if(s.charAt(low)=='(') {
                tree[treein] = new Pair(1,0);
            }
            else {
                tree[treein] = new Pair(0,1);
            }
            return;
        }
        int mid = (low+high)>>1;
        build(2*treein, low, mid);
        build(2*treein+1, mid+1, high);
        tree[treein] = merge(tree[2*treein], tree[2*treein+1]);
    }
    static Pair query(int l, int r) {
        return query(1,0,n-1,l,r);
    }
    static Pair query(int treein, int low, int high, int l, int r) {
        if(low>r || high<l) {
            return new Pair(0,0);
        }
        if(l<=low && high<=r) {
            return tree[treein];
        }
        int mid = (low+high)>>1;
        return merge(query(2*treein, low, mid, l, r), query(2*treein+1, mid+1, high,l, r));
    }
    // )(   )(
    static Pair merge(Pair a, Pair b) {
        if(a==null) {
            if(b==null) {
                return new Pair(0,0);
            }
            else {
                return b;
            }
        }
        else if(b==null) {
            return a;
        }
        if(a.nOpenBrackets>b.nCloseBrackets) {
            return new Pair(a.nOpenBrackets - b.nCloseBrackets + b.nOpenBrackets, a.nCloseBrackets);
        }
        else {
            return new Pair(b.nOpenBrackets, a.nCloseBrackets + b.nCloseBrackets - a.nOpenBrackets);
        }
    }
    static class Pair {
        int nOpenBrackets, nCloseBrackets;
        Pair(int nOpenBrackets, int nCloseBrackets) {
            this.nOpenBrackets = nOpenBrackets;
            this.nCloseBrackets = nCloseBrackets;
        }
    }
}