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 java.math.BigInteger;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		InputReader in = new InputReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		new Task().go(in, out);
		out.close();
	}

}

class Task {
	public int maxn = 1000010;
	public static class Vertex {
		int a, b, c;
		public Vertex() {a = 0; b = 0; c = 0; }
	}
	public static Vertex sum(Vertex a, Vertex b) {
		int t = Math.min(a.b, b.c);
		Vertex res = new Vertex();
		res.a = a.a + b.a + t;
		res.b = a.b + b.b - t;
		res.c = a.c + b.c - t;
		return res;
	}
	 
	Vertex[] v = new Vertex[maxn<<2];
	int n;
	String s = null;
	
	public void go(InputReader in, PrintWriter out) {
		s = in.next();
		n = s.length() - 1;
		update(0, n, 1);
		int m = in.nextInt();
		for(int i=0; i<m; i++) {
			int l = in.nextInt() - 1, r = in.nextInt() - 1;
			out.println(ask(l, r, 0, n, 1).a * 2);
		}
	}
	
	public void update(int l, int r, int rt) {
		if(l==r) {
			v[rt] = new Vertex();
			if(s.charAt(l)==')') v[rt].c++;
			else v[rt].b++;
		}
		else {
			int m = (l+r)>>1;
			update(l, m, rt<<1);
			update(m+1, r, rt<<1|1);
			v[rt] = sum(v[rt<<1], v[rt<<1|1]);
		}
	}
	
	public Vertex ask(int x, int y, int l, int r, int rt) {
		if(x<=l && y>=r) return v[rt];
		else {
			int m = (l+r)>>1;
			Vertex res = new Vertex();
			if(x<=m) res = ask(x, y, l, m, rt<<1);
			if(y>m) res = sum(res, ask(x, y, m+1, r, rt<<1|1));
			return res;
		}
	}
}

class InputReader {
	BufferedReader bf;
	StringTokenizer st;

	InputReader(InputStreamReader is) {
		bf = new BufferedReader(is);
	}

	public String next() {
		if (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(bf.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

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

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

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