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.util.Arrays;
import java.util.StringTokenizer;

public class ProblemC {
	static int[] segmentTree;
	static void singleUpdate(int position,int n) {
		for(position+=n;position>0;position/=2) {
			segmentTree[position]++;
		}
	}
	static int singleQuery(int position,int n) {
		int ans = 0;
		if(position<0) return ans;
		position++;
		int left = n;
		for(position+=n;position>left;position/=2,left/=2) {
			if(left%2!=0) ans+=segmentTree[left++];
			if(position%2!=0) ans+=segmentTree[--position];
		}
		return ans;
	}
	public static void main(String[] args) {
		InputStream in = System.in;
		InputReader scan = new InputReader(in);
		String bracSeq = scan.next();
		int len = bracSeq.length();
		segmentTree = new int[2 * len];
		
		int noOfNonMatchedOpen = 0;
		int[] nonMatchedOpenIndxs = new int[len];
		
		int[] matchedOpenIndxs = new int[len];
		int[] matchedCloseIndxs = new int[len];
		int noOfMatches = 0;
		
		for (int i = 0; i < len; i++) {
			if (bracSeq.charAt(i) == '(') {
				nonMatchedOpenIndxs[noOfNonMatchedOpen] = i;
				noOfNonMatchedOpen++;
			} else {
				if(noOfNonMatchedOpen==0) continue;
				noOfNonMatchedOpen--;
				matchedOpenIndxs[noOfMatches] = nonMatchedOpenIndxs[noOfNonMatchedOpen];
				matchedCloseIndxs[noOfMatches] = i;
				noOfMatches++;
			}
		}
		int m = scan.nextInt();
		Query[] qryArr = new Query[m];
		for (int i = 0; i < m; i++) {
			int left = scan.nextInt();
			int right = scan.nextInt();
			qryArr[i] = new Query(left-1,right-1,i);
		}
		Arrays.sort(qryArr);
		
		int j=0;
		int[] ansArr = new int[m];
		for (int i = 0; i < m; i++) {
			while(j<noOfMatches && matchedCloseIndxs[j]<=qryArr[i].right) {
				singleUpdate(matchedOpenIndxs[j],len);
				j++;
			}
			ansArr[qryArr[i].index] = singleQuery(qryArr[i].right,len) - singleQuery(qryArr[i].left-1,len);
		}
		for (int i = 0; i < m; i++) {
			int res = 2*ansArr[i];
			System.out.println(res);
		}
	}
	static class Query implements Comparable<Query> {
        int left, right, index;

        public Query(int left, int right, int ind) {
            this.left = left;
            this.right = right;
            this.index = ind;
        }

        @Override
        public int compareTo(Query o) {
            return Integer.compare(right, o.right);
        }

    }
}

class InputReader {
	BufferedReader br;
	StringTokenizer st;

	InputReader(InputStream in) {
		br = new BufferedReader(new InputStreamReader(in));
	}

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

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