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;
const int N = 1e6 + 5;
int op[4 * N], cl[4 * N];
string in;
pair<int, int> mrg(pair<int, int> a, pair<int, int> b) {
  int mn = min(a.first, b.second);
  return make_pair(a.first + b.first - mn, a.second + b.second - mn);
}
void bld(int p, int s, int e) {
  if (s == e) {
    if (in[s] == '(')
      op[p] = 1;
    else
      cl[p] = 1;
    return;
  }
  int m = (s + e) >> 1, a = p << 1, b = a | 1;
  bld(a, s, m);
  bld(b, m + 1, e);
  pair<int, int> tmp = mrg({op[a], cl[a]}, {op[b], cl[b]});
  op[p] = tmp.first;
  cl[p] = tmp.second;
}
pair<int, int> qry(int p, int s, int e, int l, int r) {
  if (s > r || e < l) return make_pair(0, 0);
  if (s >= l && e <= r) return make_pair(op[p], cl[p]);
  int m = (s + e) >> 1, a = p << 1, b = a | 1;
  return mrg(qry(a, s, m, l, r), qry(b, m + 1, e, l, r));
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> in;
  bld(1, 0, in.size() - 1);
  int q;
  cin >> q;
  while (q--) {
    int l, r;
    cin >> l >> r;
    pair<int, int> tmp = qry(1, 0, in.size() - 1, l - 1, r - 1);
    cout << r - l + 1 - tmp.first - tmp.second << '\n';
  }
  return 0;
}
