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.InputStreamReader;
import java.util.StringTokenizer;
 
public class SerejaBrackets {
	static int n;
	static int[] tree;
	
	//referred Professors code
	static void build(int[] aa) {
		for (int i=0;i<n;i++)
			tree[n + i] = aa[i];
		for (int i = n - 1; i > 0; i--)
			tree[i] = Math.min(tree[i << 1] , tree[i << 1 | 1]);
	}
	static int query(int l, int r) {
		int a = 0x3f3f3f3f;
		for (l+=n, r+=n; l<=r; l>>=1, r>>=1) {
			if ((l&1)==1)
				a = Math.min(a, tree[l++]);
			if ((r & 1) == 0)
				a = Math.min(a, tree[r--]);
		}
		return a;
	}
	
	public static void main(String[] $) throws NumberFormatException, IOException {
		int a=0;
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		char ss[] = br.readLine().toCharArray();
		n = ss.length+1;
		int[] aa = new int[n];
		for (int i=1; i<n; i++) {
			if (ss[i-1] == '(')
				a++;
			else
				a--;
			aa[i] = a;
		}
		tree = new int[2*n];
	
		build(aa);
		int m = Integer.parseInt(br.readLine());
		while (m-- > 0) {
			StringTokenizer st = new StringTokenizer(br.readLine());
			int l = Integer.parseInt(st.nextToken()) - 1;
			int r = Integer.parseInt(st.nextToken());;
			a = query(l, r);
			System.out.println(r-l-(aa[l]-a)-(aa[r]-a));
		}
	}
}