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 «()(())(())».
//package cf223;

import java.util.*;
import java.io.*;

public class C {
	FastScanner in;
	PrintWriter out;

	int[] t;

	int findMin(int v, int tl, int tr, int l, int r) {
		if (l > r)
			return Integer.MAX_VALUE;
		if (l == tl && r == tr)
			return t[v];
		int tm = (tl + tr) / 2;
		return Math.min(findMin(v * 2, tl, tm, l, Math.min(r, tm)),
				findMin(v * 2 + 1, tm + 1, tr, Math.max(l, tm + 1), r));
	}

	public void solve() throws IOException {
		String s = in.next();
		int n = s.length();
		int[] bal = new int[n];
		for (int i = 0; i < n; i++) {
			if (i == 0) {
				bal[i] = (s.charAt(i) == '(' ? 1 : -1);
			} else {
				bal[i] = bal[i - 1] + (s.charAt(i) == '(' ? 1 : -1);
			}
		}
		int k = 1;
		while (k < 2 * n) {
			k = k * 2;
		}
		t = new int[k];
		for (int i = k / 2; i < k / 2 + n; i++) {
			t[i] = bal[i - k / 2];
		}
		for (int i = k / 2 + n; i < k; i++) {
			t[i] = Integer.MAX_VALUE;
		}
		for (int i = k / 2 - 1; i >= 1; i--) {
			t[i] = Math.min(t[2 * i], t[2 * i + 1]);
		}
		int m = in.nextInt();
		for (int i = 0; i < m; i++) {
			int l = in.nextInt() - 1;
			int r = in.nextInt() - 1;
			int len = (r - l) + 1;
			int d = bal[r] - ((l == 0)? 0 : bal[l - 1]);
			int z = (len - d) / 2;
			int min = findMin(1, 0, k / 2 - 1 , l, r) - ((l == 0)? 0 : bal[l - 1]);
			System.out.println((z + Math.min(0, min)) * 2);
		}
	}

	public void run() {
		try {
			in = new FastScanner(System.in);
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

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

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

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

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

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

	public static void main(String[] arg) {
		new C().run();
	}
}