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 SegmentTreeBracket {
    private static String s;
    private static int[] valids;
    private static int[] leftBrackets;
    private static int[] rightBrackets;

    private static int[] v;
    private static int[] l;
    private static int[] r;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        
        s = sc.next();
        int n = sc.nextInt();
        valids = new int[4 * s.length()];
        leftBrackets = new int[4 * s.length()];
        rightBrackets = new int[4 * s.length()];
        v = new int[4 * s.length()];
        l = new int[4 * s.length()];
        r = new int[4 * s.length()];

        build(1, 0, s.length());

        for (int i = 0; i < n; i++) {
            // 1<=left<=right<=n
            int left = sc.nextInt();
            int right = sc.nextInt();
            search(left - 1, right, 1, 0, s.length());
            out.println(v[1]);
        }
        out.close();
    }

    // [left, right)
    private static void build(int id, int left, int right) {
        if (left + 1 == right) {
            if (s.charAt(left) == '(')
                leftBrackets[id]++;
            else
                rightBrackets[id]++;
            return;
        }

        int mid = (left + right) / 2;
        build(id * 2, left, mid);
        build(id * 2 + 1, mid, right);

        int min = Math.min(leftBrackets[id * 2], rightBrackets[id * 2 + 1]);
        valids[id] = valids[id * 2] + valids[id * 2 + 1] + 2 * min;
        leftBrackets[id] = leftBrackets[id * 2] - min
                + leftBrackets[id * 2 + 1];
        rightBrackets[id] = rightBrackets[id * 2] + rightBrackets[id * 2 + 1]
                - min;
    }

    // [left, right)
    private static void search(int x, int y, int id, int left, int right) {
        if (right <= x || left >= y){
            l[id] = 0;
            r[id] = 0;
            v[id] = 0;
            return;
        }
        if (left >= x && right <= y){
            v[id] = valids[id];
            l[id] = leftBrackets[id];
            r[id] = rightBrackets[id];
            return;
        }

        int mid = (left + right) / 2;
        search(x, y, id * 2, left, mid);
        search(x, y, id * 2 + 1, mid, right);
        
        int min = Math.min(l[id*2], r[id*2+1]);
        v[id] = v[id * 2] + v[id * 2 + 1] + 2 * min;
        l[id] = l[id * 2] - min + l[id * 2 + 1];
        r[id] =  r[id * 2] + r[id * 2 + 1] - min;
    }

       //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
      try {
         str = br.readLine();
      } catch (IOException e) {
         e.printStackTrace();
      }
      return str;
      }

   }
}