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;
string s;
pair<int, pair<int, int>> st[4000005];
pair<int, pair<int, int>> build(int i, int l, int r) {
  if (l + 1 == r) return st[i] = {0, {s[l] == '(', s[l] == ')'}};
  int mid = l + (r - l) / 2;
  auto t1 = build(i * 2, l, mid), t2 = build(i * 2 + 1, mid, r);
  st[i] = {t1.first + t2.first + min(t1.second.first, t2.second.second),
           {t1.second.first + t2.second.first -
                min(t1.second.first, t2.second.second),
            t1.second.second + t2.second.second -
                min(t1.second.first, t2.second.second)}};
  return st[i];
}
pair<int, pair<int, int>> query(int i, int l, int r, int s, int e) {
  if (s <= l && r <= e) return st[i];
  if (e <= l || s >= r) return {0, {0, 0}};
  int mid = l + (r - l) / 2;
  auto t1 = query(i * 2, l, mid, s, e), t2 = query(i * 2 + 1, mid, r, s, e);
  return {t1.first + t2.first + min(t1.second.first, t2.second.second),
          {t1.second.first + t2.second.first -
               min(t1.second.first, t2.second.second),
           t1.second.second + t2.second.second -
               min(t1.second.first, t2.second.second)}};
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> s;
  int n = s.length(), m;
  cin >> m;
  build(1, 0, n);
  int l, r;
  while (m--) {
    cin >> l >> r;
    l--, r--;
    cout << query(1, 0, n, l, r + 1).first * 2 << '\n';
  }
}
