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.io.PrintWriter;
import java.util.StringTokenizer;



public class Solution {
	static int N, o[], c[], t[];
	static char str[];
    static class Triplet {
    	int tot, open, close;
    
    	Triplet(int a, int b, int c) {
    		tot = a;
    		open = b;
    		close = c;
    	}
    }
	public static void build(int id, int l, int r) {
		if (l == r) {
			if (str[l] == '(') {
				o[id] = 1;
			} else
				c[id] = 1;
			return;
		}
		int mid = (l + r) / 2;
		build(2 * id + 1, l, mid);
		build(2 * id + 2, mid + 1, r);
		int tmp = Math.min(o[2 * id + 1], c[2 * id + 2]);
		t[id] = t[2 * id + 1] + t[2 * id + 2] + tmp;
		o[id] = o[2 * id + 1] + o[2 * id + 2] - tmp;
		c[id] = c[2 * id + 1] + c[2 * id + 2] - tmp;
	}

	public static Triplet query(int x, int y, int id, int l, int r) {
		if (l > y || r < x)
			return new Triplet(0, 0, 0);
		if (x <= l && r <= y)
			return new Triplet(t[id], o[id], c[id]);
		int mid = (l + r) / 2;
		Triplet a = query(x, y, 2 * id + 1, l, mid);
		Triplet b = query(x, y, 2 * id + 2, mid + 1, r);
		int T, temp, O, C;
		temp = Math.min(a.open, b.close);
		T = a.tot + b.tot + temp;
		O = a.open + b.open - temp;
		C = a.close + b.close - temp;
		return new Triplet(T, O, C);
	}

	public static void main(String[] args) throws Exception {
		InputReader in = new InputReader();
		PrintWriter out = new PrintWriter(System.out);
		str = in.next().toCharArray();
		N = str.length;
		int sz = (int) Math.pow(2, (Math.log(N) / Math.log(2)) + 1);
		sz = sz * 2;
		o = new int[sz];
		c = new int[sz];
		t = new int[sz];
		build(0, 0, N - 1);
		int M = in.nextInt();
		int x, y;
		StringBuilder sb = new StringBuilder();
		while (M-- > 0) {
			x = in.nextInt() - 1;
			y = in.nextInt() - 1;
			Triplet a = query(x, y, 0, 0, N - 1);
			int ans = a.tot * 2;
			sb.append(ans + "\n");
			if (sb.length() > 1000) {
				System.out.print(sb.toString());
				sb = new StringBuilder();
			}
		}
		System.out.print(sb.toString());
	}

	static class InputReader {
		BufferedReader br;
		StringTokenizer st;

		public InputReader() {
			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;
		}
	}
}
