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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class SerejaandBrackets2 {
	static final int INF = (int) 1e7;
	static int n;
	static int ans = 0;

	public static void main(String[] args) throws IOException {

		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		String s = sc.next();
		n = s.length();

		int N = 1;
		while (N < n)
			N <<= 1; // padding

		char[] in = new char[N + 1];

		for (int i = 0; i < s.length(); i++)
			in[i + 1] = s.charAt(i);
		SegmentTree st = new SegmentTree(in);

		int q = sc.nextInt();
		while (q-- > 0) {
			ans = 0;
			int l = sc.nextInt();
			int r = sc.nextInt();
			
			pw.println(st.query(l, r).len);
		}
		pw.flush();
		pw.close();
	}

	static class Node {

		int remopen;
		int remclosed;
		int len = 0;

		public Node() {

		}

//		public String toString() {
//			return "ro " + remopen + " rc " + remclosed + " len " + len;
//		}

	}

	static class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		char[] array;
		Node[] sTree;

		SegmentTree(char[] in) {
			array = in;
			N = in.length - 1;
			sTree = new Node[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero

			for (int i = 0; i < (N << 1); i++) {
				sTree[i] = new Node();

			}
			build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e) {
				if (array[b] == ')')
					sTree[node].remopen = 1;
				else
					sTree[node].remclosed = 1;
			} else {

				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);

				
				sTree[node].len = sTree[node << 1].len + sTree[node << 1 | 1].len
						+ 2 * Math.min(sTree[node << 1].remclosed, sTree[node << 1 | 1].remopen);
				sTree[node].remclosed = sTree[node << 1].remclosed + sTree[node << 1 | 1].remclosed
						- Math.min(sTree[node << 1].remclosed, sTree[node << 1 | 1].remopen);
				sTree[node].remopen = sTree[node << 1].remopen + sTree[node << 1 | 1].remopen
						- Math.min(sTree[node << 1].remclosed, sTree[node << 1 | 1].remopen);
			}
		}

		Node query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		Node query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b) {
				return new Node();
			}
			if (b >= i && e <= j) {
				return sTree[node];
			}

			int mid = b + e >> 1;
			Node q1 = query(node << 1, b, mid, i, j);

			Node q2 = query(node << 1 | 1, mid + 1, e, i, j);
			
			
			ans= q1.len + q2.len+2*Math.min(q1.remclosed, q2.remopen);
			Node temp = new Node();
			temp.len=ans;
			temp.remclosed=q1.remclosed+q2.remclosed-Math.min(q1.remclosed, q2.remopen);
			temp.remopen=q1.remopen+q2.remopen-Math.min(q1.remclosed, q2.remopen);
			return temp;
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

	}
}
