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.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;


public class E_223 {

	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	
	static String readString() throws Exception {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(stdin.readLine());
		return st.nextToken();
	}

	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	static long readLong() throws Exception {
		return Long.parseLong(readString());
	}
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		String s = readString();
		int n = s.length();
		int ls[] = new int[n+1];
		int rs[] = new int[n+1];
		int a[] = new int[n+1];
		Tree tree = new Tree();
		for(int i = 1; i < n+1; i++){
			char c = s.charAt(i-1);
			if(c == '('){
				a[i] = a[i-1]+1;
				ls[i] = ls[i]+1;
				rs[i] = rs[i-1];
			}
			else{
				a[i] = a[i-1]-1;
				ls[i] = ls[i];
				rs[i] = rs[i-1]+1;
			}
			tree.update(i, a[i]);
		}
		int m = readInt();
		for(int i = 0; i < m; i++){
			int l = readInt();
			int r = readInt();
			int before = a[l-1];
			int intervalMin = tree.query(l, r);
			int tooMuch = intervalMin-before;
			if(tooMuch < 0){
				System.out.println(2*(rs[r]-rs[l-1]+tooMuch));
			} else{
				System.out.println(2*(rs[r]-rs[l-1]));
			}
		}
	}
	
	static class Tree {
		//Space used is offset,offset + size of table
		private int OFFSET = 1000001;
		private int tree[];	

		// Add v to cell i. Max, min and gcd in interval in comments
		public void update(int i, int v) {
		    i += OFFSET;
		    tree[i] = v; 
		    i /= 2;
		    while(i > 0) {
		        tree[i] = Math.min(tree[2*i], tree[2*i+1]);
													//gcd: tree[i] = gcd(tree[2*i], tree[2*i+1]);
		        i /= 2;
		    }
		}

		// Get sum in interval l (inclusive) to r (inclusive)
		public int query(int l, int r) {
		    int result = Integer.MAX_VALUE;
		    l += OFFSET - 1; r+= OFFSET+1;
		    while(l/2 != r/2) {
		        if(l%2 == 0) result = Math.min(result, tree[l^1]);
													//gcd: result = gcd(result, tree[l^1]);
				if(r%2 == 1) result = Math.min(result, tree[r^1]);
													//gcd: result = gcd(result, tree[r^1]);
		 		l /= 2; r /= 2;
		    }
		    return result;
		}
		
		public Tree(){
			tree = new int[2*OFFSET];
		}
	}

}
