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 Slow {
	public static Scanner stdin = null;
	public static PrintWriter stdout = null;
	public static Vertex[] t = new Vertex[10000000];

	public static class Vertex {
		public int a;
		public int b;
		public int c;
		public Vertex () {
			a = 0;
			b = 0;
			c = 0;
		}
	}

	public static Vertex sum(Vertex v1, Vertex v2) {
		Vertex temp = new Vertex();
		int t = Math.min(v1.b, v2.c);
		temp.a = v1.a + v2.a + t;
		temp.b = v1.b + v2.b - t;
		temp.c = v1.c + v2.c - t;
		return temp;
	}

	public static void build(String s, int v, int tl, int tr) {
		if (tl == tr) {
			t[v] = new Vertex();
			if (s.charAt(tl) == '(') { 
				t[v].b = 1;
			} else {
				t[v].c = 1;
			}
		} else {
			int tm = (tl + tr) / 2;
			build(s, 2 * v, tl, tm);
			build(s, 2 * v + 1, tm + 1, tr);
			t[v] = sum(t[2 * v], t[2 * v + 1]);
		}
	}
	
	public static Vertex find(int v, int tl, int tr, int l, int r) {
		if (l > r) return new Vertex();
		if (tl == l && tr == r) return t[v];

		int tm = (tl + tr) / 2;
        return sum(find(2 * v, tl, tm, l, Math.min(tm, r)), find(2 * v + 1, tm + 1, tr, Math.max(l, tm + 1), r));
	}

	public static void main(String[] args) throws FileNotFoundException {
		stdin = new Scanner(System.in);
		stdout = new PrintWriter(System.out);
		
		String s = stdin.nextLine();
		build(s, 1, 0, s.length() - 1);
		
		int n = stdin.nextInt();
		for (int i = 0; i < n; i++) {
			int l = stdin.nextInt();
			int r = stdin.nextInt();
			Vertex vertex = find(1, 0, s.length() - 1, l - 1, r - 1);
			stdout.println(2 * vertex.a);
		}
		
		stdin.close();
		stdout.flush();
		stdout.close();
	}
}
