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 «()(())(())».
#include <bits/stdc++.h>
using namespace std;
int sa[4 * 1000005];
int so[4 * 1000005];
int sc[4 * 1000005];
string str;
int N;
void build(int low, int high, int i) {
  if (low == high) {
    sa[i] = 0;
    if (str[low] == '(') {
      so[i] = 1;
      sc[i] = 0;
    } else {
      so[i] = 0;
      sc[i] = 1;
    }
    return;
  }
  int mid = low + (high - low) / 2;
  build(low, mid, 2 * i + 1);
  build(mid + 1, high, 2 * i + 2);
  int y = min(so[2 * i + 1], sc[2 * i + 2]);
  sa[i] = sa[2 * i + 1] + sa[2 * i + 2] + 2 * y;
  so[i] = so[2 * i + 1] + so[2 * i + 2] - y;
  sc[i] = sc[2 * i + 1] + sc[2 * i + 2] - y;
  return;
}
pair<int, pair<int, int>> query(int low, int high, int qs, int qe, int i) {
  if (qe < low || qs > high || low > high) {
    return {0, {0, 0}};
  }
  if (qs <= low && qe >= high) {
    return {sa[i], {so[i], sc[i]}};
  }
  int mid = low + (high - low) / 2;
  pair<int, pair<int, int>> l = query(low, mid, qs, qe, 2 * i + 1);
  pair<int, pair<int, int>> r = query(mid + 1, high, qs, qe, 2 * i + 2);
  int c = min(l.second.first, r.second.second);
  l.first = l.first + r.first + 2 * c;
  l.second.first = l.second.first + r.second.first - c;
  l.second.second = l.second.second + r.second.second - c;
  return l;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> str;
  N = str.length();
  build(0, N - 1, 0);
  int q;
  cin >> q;
  int l, r;
  for (int i = 1; i <= q; i++) {
    cin >> l >> r;
    l--;
    r--;
    cout << query(0, N - 1, l, r, 0).first << "\n";
  }
  return 0;
}
