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 C380_SerejaAndBrackets {

	public static void main(String[] args) throws IOException {
		Scanner in =new Scanner(System.in);
		StringBuilder sb =new StringBuilder();
		String s = in.nextLine();
		int N = 1;int n = s.length();
		while(N < n)	N <<= 1;
		Trio [] a=new Trio [N+1];
		
		for(int i=1;i<=s.length();i++)
			a[i] = (s.charAt(i-1)== '(' )? new Trio(1,0,0):new Trio(0,1,0);
		
		for(int i=0;i<a.length;i++)
			if(a[i] == null)
				a[i] = new Trio(0,0,0);
		
		SegmentTree st= new SegmentTree(a);
		int q=in.nextInt();
		while(q-->0)
			sb.append(st.query(in.nextInt(), in.nextInt())).append("\n");
		
		System.out.print(sb);
	}
	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();}


	}
	
	static class Trio
	{
		int op;int clos;int ressofar;
		Trio(int a, int b, int c)
		{
			op=a;clos=b;ressofar=c;
		
		}
	}
	
	static class SegmentTree{
		int N;
		Trio Stree[];Trio [] arr;
		
		SegmentTree(Trio []a)
		{
			arr=a;
			N = a.length-1;
			Stree = new Trio[N<<1];
			build(1,1,N);
		}
		
		void build(int node, int b, int e)
		{
			if(b == e)
			{
				 Stree[node] = new Trio(arr[b].op, arr[b].clos, arr[b].ressofar);
			}
			else
			{
			build((node<<1), b, (b+e)/2);
			build((node<<1)+1, (b+e)/2+1, e);
			Trio left =Stree[node<<1];
			Trio right =Stree[(node<<1)+1];
			int res = Math.min(left.op, right.clos);
			int open = left.op + right.op - res;
			int close = left.clos + right.clos - res;
			
			Stree[node] = new Trio(open, close, res*2+left.ressofar+right.ressofar);
			}
		}
		
		int query(int i,int j)
		{
			return query(1,1,N,i,j).ressofar;
		}
		
		Trio query(int node, int b, int e, int i, int j)
		{
			if(i>e || j <b)
				return new Trio(0,0,0);	
			
			if(b>= i && e <= j)
				return Stree[node];
			
			Trio left = query(node<<1,b,(b+e)/2,i,j);
			Trio right = query((node<<1)+1,(b+e)/2+1,e,i,j);
			int res = Math.min(left.op, right.clos);
			int open = left.op + right.op - res;
			int close = left.clos + right.clos - res;
			
			return  new Trio(open, close, res*2+left.ressofar+right.ressofar);

		}
		
	}
}
