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;
struct SegmentTree {
  SegmentTree *left, *right;
  int start, end;
  int value;
  int open, close;
  SegmentTree(int l, int r)
      : start(l),
        end(r),
        left(NULL),
        right(NULL),
        value(0),
        open(0),
        close(0) {}
  void build(string &s) {
    if (start == end) {
      if (s[start - 1] == '(') {
        open++;
      } else
        close++;
    } else {
      int mid = (start + end) >> 1;
      left = new SegmentTree(start, mid);
      right = new SegmentTree(mid + 1, end);
      left->build(s);
      right->build(s);
      value = right->value + left->value + 2 * min(left->open, right->close);
      close = right->close + left->close - min(left->open, right->close);
      ;
      open = right->open + left->open - min(left->open, right->close);
      ;
    }
  }
  int query(int l, int r, vector<SegmentTree *> &v) {
    if (r < start || end < l) return 0;
    if (l <= start && end <= r) {
      v.push_back(this);
      return value;
    }
    return left->query(l, r, v) + right->query(l, r, v);
  }
};
SegmentTree *merge(SegmentTree *node, SegmentTree *node2) {
  SegmentTree *nodeA = new SegmentTree(1, 1);
  nodeA->value = node->value + node2->value + 2 * min(node->open, node2->close);
  nodeA->close = node->close + node2->close - min(node->open, node2->close);
  ;
  nodeA->open = node->open + node2->open - min(node->open, node2->close);
  ;
  return nodeA;
}
void solve() {
  string s;
  cin >> s;
  int q;
  int l, r;
  SegmentTree *segmentTree = new SegmentTree(1, s.size());
  segmentTree->build(s);
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> l >> r;
    vector<SegmentTree *> v;
    segmentTree->query(l, r, v);
    SegmentTree *node = v[0];
    for (int i = 1; i < v.size(); i++) {
      node = merge(node, v[i]);
    }
    cout << node->value << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
  return 0;
}
