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.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class TestClass {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	
	public static class Pair implements Comparable<Pair> {
		long u;
		long v;
		public Pair(long u, long v) {
			this.u = u;
			this.v = v;
		}
		public int hashCode() {
			int hu = (int) (u ^ (u >>> 32));
			int hv = (int) (v ^ (v >>> 32));
			return 31 * hu + hv;
		}
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return u == other.u && v == other.v;
		}
		public int compareTo(Pair other) {
			return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
		}
		public String toString() {
			return u+" "+v;
		}
	}
	static Pair p[] = new Pair[10000000];
	public static void Build(int l,int r,int c,String a){
		if(l==r){
			long op = 0;
			if(a.charAt(l)=='(')
				op = ((long)1)<<32;
			else
				op = 1;
			p[c] = new Pair(op,0);
			return ;
		}
		int mid = (l+r)>>1;
		Build(l,mid,2*c+1,a);
		Build(mid+1,r,2*c+2,a);
		p[c] = combine(p[2*c+1],p[2*c+2]);
	}
	public static Pair combine(Pair a,Pair b){
		long kl = 2*Math.min((a.u>>32),(int) b.u);
		long open = (a.u>>32) + (b.u>>32) - kl/2;
		long close = (int)a.u + (int)b.u - kl/2;
		return new Pair((open<<32)|close,a.v+b.v+kl);
	}
	public static Pair get(int l,int r,int c,int x,int y){
		if(l>r||x>y||l>y||x>r)
			return new Pair(0,0);
		if(x<=l&&y>=r)
			return p[c];
		int mid = (l+r)>>1;
		Pair a1 = get(l,mid,2*c+1,x,y);
		Pair a2 = get(mid+1,r,2*c+2,x,y);
		return combine(a1,a2);
	}
	private static void soln(){
		String a = nLi();
		Build(0,a.length()-1,0,a);
		int m = nI();
		while(m-->0){
			int x = nI()-1,y = nI()-1;
			pw.println(get(0,a.length()-1,0,x,y).v);
		}
	}

	public static void main(String[] args) {
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		soln();
		pw.close();
	}

	// To Get Input
	// Some Buffer Methods
	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private static int nI() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static long nL() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static String nLi() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}