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.Scanner;
import java.util.StringTokenizer;

public class C380 {
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		String s = sc.next();
		s = '@'+s;
		
		SegmentTree st = new SegmentTree(s);
		
		int m = sc.nextInt();
		
		while(m-->0)
			pw.println(st.query(sc.nextInt(), sc.nextInt()).max);
		
		pw.flush();
	}
	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)
		Node[] sTree;
		String array;
		
		SegmentTree(String in)		
		{
			array = in;
			N = 1;
			
			while(N<array.length()){N<<=1;}
			
			sTree = new Node[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
			build(1,1,N);
		}
		
		void build(int node, int b, int e)	// O(n)
		{
			if(b == e)			
				sTree[node] = new Node(0,b>=array.length()?0:(array.charAt(b)=='('?1:0),b>=array.length()?0:(array.charAt(b)==')'?1:0));
			else						
			{
				int mid = b + e >> 1;
				build(node<<1,b,mid);
				build(node<<1|1,mid+1,e);
				
				int max = sTree[node<<1].max+sTree[node<<1|1].max;
				
				max += Math.min(sTree[node<<1].opened, sTree[node<<1|1].closed)*2;
				
				int opened = sTree[node<<1].opened+sTree[node<<1|1].opened-Math.min(sTree[node<<1].opened, sTree[node<<1|1].closed);
				int closed =  sTree[node<<1].closed+sTree[node<<1|1].closed-Math.min(sTree[node<<1].opened, sTree[node<<1|1].closed);
				
				sTree[node] = new Node(max,opened,closed);
			}
		}
		
		
//		void update_point(int index, int val)			// O(log n)
//		{
//			index += N - 1;				
//			sTree[index] += val;			
//			while(index>1)				
//			{
//				index >>= 1;
//				sTree[index] = sTree[index<<1] + sTree[index<<1|1];		
//			}
//		}
		
		
		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(0,0,0);		
			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);
			
			int max = q1.max+q2.max;
			
			max += Math.min(q1.opened, q2.closed)*2;
			
			int opened = q1.opened+q2.opened-Math.min(q1.opened, q2.closed);
			int closed = q1.closed+q2.closed-Math.min(q1.opened, q2.closed);
			
					
			return new Node(max,opened,closed);
		}
		
		
//		public static void main(String[] args) {
//			
//			Scanner sc = new Scanner(System.in);
//			
//			int n = sc.nextInt();
//			int N = 1; while(N < n) N <<= 1; //padding
//			
//			int[] in = new int[N + 1];
//			for(int i = 1; i <= n; i++)
//				in[i] = sc.nextInt();
//			
//			sc.close();
//		}
		
	}
	
	static class Node{
		int max, opened, closed;
		public Node(int m, int o, int c){
			max = m;
			opened = o;
			closed = c;
		}
	}
	
	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());}

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

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

		public double nextDouble() throws IOException
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}

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


	}
}
