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 Main {
	public static void main(String[] args) throws IOException {
		
		PrintWriter pw=new PrintWriter(System.out);
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		int n=s.length();
		int N=1;
		while(N<n) N<<=1; 
		Node[] arr = new Node[N+1];
		for(int i=1;i<=n;i++)
			if(s.charAt(i-1)=='(')
				arr[i] = new Node(1,0,0);
			else
				arr[i] = new Node(0,1,0);
		for(int i=n+1;i<=N;i++)
			arr[i] = new Node(0,0,0);
		SegmentTree st = new SegmentTree(arr);
		int m =sc.nextInt();
		for(int i=0;i<m;i++)
			pw.println(st.query(sc.nextInt(), sc.nextInt()).max);
		pw.close();
		pw.flush();

	}

	static class Node{
		int start,end,max;

		public Node(int a, int b , int c)
		{
			start=a;
			end=b;
			max=c;
		}
		
		public String toString()
		{
			return""+ max ;  
		}
	}

	static class SegmentTree{

		int N;
		Node[] st , arr;

		public SegmentTree(Node[] arr)
		{
			 N =arr.length-1;
			this.arr = arr;
			st = new Node[N<<1];
			build(1,1,N);
		}

		void build(int node,int b , int e)
		{
			//System.out.println(node +"   "+ b + "  "+  e);
			if(b==e)
				st[node]=arr[b];
			else
			{
				int mid=(b+e)/2;
				build(node<<1,b,mid);
				build((node<<1)+1,mid+1,e);
				st[node] =combine(st[node<<1] , st[(node<<1)+1]);
			}
		}

		Node combine(Node left, Node right)
		{
			int min = Math.min(left.start,right.end);
			return new Node(left.start+right.start-min,right.end+left.end-min,left.max+right.max+min*2);
		}

		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)
		{
			//System.out.println(node + "  " + b + "  " + e + "  " + i + "   "+ j );
			//System.out.println(N);
			if(i>e || j<b)
				return new Node(0,0,0);
			if(b>=i && e<=j)
			{
				//System.out.println(st[node]);
				return st[node];
			}

			int mid = (b+e)/2;
			Node q1= query(node<<1,b,mid,i,j);
			Node q2= query((node<<1)+1,mid+1,e,i,j);
			//System.out.println(q1+"  " + q2);
			return combine(q1 , q2);
		}
	}

	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();}
	}

}