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.StringTokenizer;

public class Serjiaandbrackets {

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

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		String s = sc.nextLine();
		int n = s.length();

		int q = sc.nextInt();

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

		char[] in = new char[N + 1];
		for (int i = 1; i <= n; i++)
			in[i] = s.charAt(i - 1);

		SegmentTree st = new SegmentTree(in);
		while (q-- > 0) {
			out.println(st.query(sc.nextInt(), sc.nextInt()));
		}
		out.flush();
		out.close();

	}

	static class pair {
		int left, right;
		int n;

		pair(int l, int r, int x) {
			left = l;
			right = r;
			n = x;

		}
	}

	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)
		pair[] sTree, lazy;
		char[] array;

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

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				if (array[b] == '(')
					sTree[node] = new pair(0, 1, 0);
				else
					sTree[node] = new pair(1, 0, 0);

			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				pair left = sTree[node << 1];
				pair right = sTree[node << 1 | 1];
				int valid = Math.min(left.right, right.left);

				sTree[node] = new pair(left.left + right.left - valid, right.right + left.right - valid,
						valid * 2 + left.n + right.n);
			}
		}

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

		pair query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return new pair(0, 0, 0);
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			pair left = query(node << 1, b, mid, i, j);
			pair right = query(node << 1 | 1, mid + 1, e, i, j);
			int valid = Math.min(left.right, right.left);

			return new pair(left.left + right.left - valid, right.right + left.right - valid,
					valid * 2 + left.n + right.n);

		}

	}

	static class Scanner {

		StringTokenizer st;
		BufferedReader br;

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() {
			for (long i = 0; i < 3e9; i++)
				;
		}
	}

}