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 «()(())(())».

//http://codeforces.com/contest/381/problem/E
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class SerejaAndBrackets {

	public static class SegmentTree {

		public Node[] segTree;
		public String brackets;
		public int height, maxsize;

		public SegmentTree(String brackets) {
			this.brackets = brackets;
			height = (int) (Math.ceil(Math.log(brackets.length()) / Math.log(2)));
			maxsize = 2 * (int) Math.pow(2, height) - 1;
			segTree = new Node[maxsize];
		}

		public void build(int low, int high, int pos) {
			if (low == high) {
				if (brackets.charAt(low) == ')')
					segTree[pos] = new Node(0, 1, 0);
				else
					segTree[pos] = new Node(1, 0, 0);
				return;
			}
			int mid = (low + high) / 2;
			build(low, mid, 2 * pos + 1);
			build(mid + 1, high, 2 * pos + 2);
			Node temp1 = segTree[2 * pos + 1];
			Node temp2 = segTree[2 * pos + 2];
			int max = temp1.Combination + temp2.Combination;
			int temp = Math.min(temp1.LeftBrackets, temp2.RightBrackets);
			segTree[pos] = new Node(temp1.LeftBrackets + temp2.LeftBrackets - temp,
					temp1.RightBrackets + temp2.RightBrackets - temp, max + (temp * 2));
		}

		public Node RangeSumQuery(int a, int b, int low, int high, int pos) {
			if (a <= low && b >= high)
				return segTree[pos];
			if (a > high || b < low)
				return new Node(0, 0, 0);

			int mid = (low + high) / 2;
			Node temp1 = RangeSumQuery(a, b, low, mid, 2 * pos + 1);
			Node temp2 = RangeSumQuery(a, b, mid + 1, high, 2 * pos + 2);
			int max = temp1.Combination + temp2.Combination;
			int temp = Math.min(temp1.LeftBrackets, temp2.RightBrackets);
			return new Node(temp1.LeftBrackets + temp2.LeftBrackets - temp,
					temp1.RightBrackets + temp2.RightBrackets - temp, max + temp * 2);
		}

	}

	public static class Node {
		int LeftBrackets;
		int RightBrackets;
		int Combination;

		public Node(int LeftBrackets, int RightBrackets, int Combination) {
			this.LeftBrackets = LeftBrackets;
			this.RightBrackets = RightBrackets;
			this.Combination = Combination;
		}
	}

	public static void main(String[] args) {
		FastScanner scan = new FastScanner(System.in);
		String str = scan.next();
		SegmentTree st = new SegmentTree(str);
		st.build(0, str.length() - 1, 0);
		int Q = scan.nextInt();
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < Q; i++) {
			sb.append(st.RangeSumQuery(scan.nextInt() - 1, scan.nextInt() - 1, 0, str.length() - 1, 0).Combination);
			sb.append("\n");
		}
		System.out.println(sb);
	}

	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public FastScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

}
