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.util.*;
import java.io.*;
public class cf {
	static class help{
		int corr ,right ,left;
		public help(int c ,int r ,int l) {
			// TODO Auto-generated constructor stub
			corr=c;
			right=r;
			left=l;
		}
		public String toString()
		{
			return corr+" "+right+" "+left;
		}
	}
  public static void main(String[] args) throws IOException,InterruptedException{
	Scanner sc =new Scanner(System.in);
	PrintWriter pw = new PrintWriter(System.out);
	char[]arr =sc.next().toCharArray();
	int N=1;
	while (arr.length>N)
		N<<=1;
	help[] x =new help[N+1];
	for (int i =1;i<=N;++i)
		if (i>arr.length)
			x[i]=new help(0, 0, 0);
		else
			x[i]=new help(0, arr[i-1]=='('?1:0, arr[i-1]==')'?1:0);
		SegmentTree st =new SegmentTree(x);
		int t=sc.nextInt();
		//System.out.println(N);
		while (t-->0)
			pw.println(st.query(sc.nextInt(), sc.nextInt())*2);
     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)
		help[] array, sTree;
	 
		SegmentTree(help[] in)		
		{
			array = in; N = in.length - 1;
			sTree = new help[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] = array[b];
			else						
			{
				int mid = b + e >> 1;
				build(node<<1,b,mid);
				build(node<<1|1,mid+1,e);
				sTree[node] = add(sTree[node<<1],sTree[node<<1|1]);
			}
		}
		public help add (help a ,help b) {
			int min =Math.min(a.right, b.left);
			return new help(a.corr+b.corr+min, a.right+b.right-min, a.left+b.left-min);
		}
		int query(int i, int j)
		{
			return query(1,1,N,i,j).corr;
		}
	 
		help query(int node, int b, int e, int i, int j)	// O(log n)
		{
			if(i>e || j <b)
				return new help(0, 0, 0);		
			if(b>= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			help q1 = query(node<<1,b,mid,i,j);
			help q2 = query(node<<1|1,mid+1,e,i,j);
			return add(q1, q2);	 
		}
	}
  static class Scanner {
		StringTokenizer stringTokenizer;
		BufferedReader bfBufferedReader;
		public Scanner(InputStream system) {
			bfBufferedReader=new BufferedReader(new InputStreamReader( system));
		}
		 public Scanner(String file) throws Exception {
	            bfBufferedReader = new BufferedReader(new FileReader( file));
	        }			 
	        public String next() throws IOException {
	            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens())
	                stringTokenizer = new StringTokenizer( bfBufferedReader.readLine());
	            return stringTokenizer.nextToken();
	        }
	 
	        public String nextLine() throws IOException {
	            return bfBufferedReader.readLine();
	        }
	 
	        public int nextInt() throws IOException {
	            return Integer.parseInt(next());
	        }
	 
	        public double nextDouble() throws IOException {
	            return Double.parseDouble(next());
	        }
	 
	        public char nextChar() throws IOException {
	            return next().charAt(0);
	        }
	 
	        public Long nextLong() throws IOException {
	            return Long.parseLong(next());
	        }
	 
	        public boolean ready() throws IOException {
	            return bfBufferedReader.ready();
	        }
	 
	        public void waitForInput() throws InterruptedException {
	            Thread.sleep(3000);
	        }
	    }
	}