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.InputStreamReader;
import java.util.Arrays;
public class Main {
    static void build(int node, node[] tree, int l, int r, String str) {
        if(l==r) {
            node n = null;
            if(str.charAt(l)=='(') {
                n = new node(0,1,0);
            } else n = new node(0,0,1);
            tree[node] = n;
            return ;
        }
        int mid = (l+r)/2;
        build(node*2,tree,l,mid,str);
        build(node*2+1,tree,mid+1,r,str);
        int t = Math.min(tree[node*2].b,tree[node*2+1].c);
        node tmp = new node(0,0,0);
        tmp.a = tree[node*2].a+t*2+tree[node*2+1].a;
        tmp.b = tree[node*2].b+tree[node*2+1].b-t;
        tmp.c = tree[node*2].c-t+tree[node*2+1].c;
        tree[node] = tmp;
    }
    static node query(int node, node[] tree, int i, int j, int l, int r) {
        if(i>r || j<l) return new node(0,0,0);
        if(i<=l && j>=r) return tree[node];
        int mid = (l+r)/2;
        node x = query(node*2,tree,i,j,l,mid);
        node y = query(node*2+1,tree,i,j,mid+1,r);
        node tmp = new node(0,0,0);
        int t = Math.min(x.b,y.c);
        tmp.a = x.a+t*2+y.a;
        tmp.b = x.b+y.b-t;
        tmp.c = x.c-t+y.c;
        return tmp;
    }
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader((System.in)));
        String str = br.readLine();
        int n = Integer.parseInt(br.readLine());
        //int rt = (int)Math.pow(2,str.length());
        node[] tree = new node[4*str.length()+1];
        Arrays.fill(tree,null);
        build(1,tree,0,str.length()-1,str);
//        for(int i=1;i<rt;i++) {
//            if (tree[i] != null) System.out.println(tree[i].a + " " + tree[i].b + " " + tree[i].c);
//        }
        StringBuilder sb = new StringBuilder();
        while(n-->0) {
            String[] s = br.readLine().split(" ");
            int l = Integer.parseInt(s[0])-1;
            int r = Integer.parseInt(s[1])-1;
            node y = query(1,tree,l,r,0,str.length()-1);
            sb.append(y.a+"\n");
        }
        System.out.print(sb);
    }
}
class node {
    int a,b,c;
    node(int a, int b, int c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }
}
