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 n, m;
int x, y;
string s;
class SegmentTree {
 private:
  vector<int> st, a, b, c;
  int left(int p) { return (p << 1); }
  int right(int p) { return (p << 1) + 1; }
  void build(int p, int l, int r) {
    if (l == r) {
      if (s[l] == '(') {
        st[p] = 0;
        a[p] = 0;
        b[p] = 1;
        c[p] = 0;
      } else {
        st[p] = 0;
        a[p] = 0;
        b[p] = 0;
        c[p] = 1;
      }
    } else {
      build(left(p), l, (l + r) / 2);
      build(right(p), (l + r) / 2 + 1, r);
      int t = min(b[left(p)], c[right(p)]);
      a[p] = a[left(p)] + a[right(p)] + t;
      b[p] = b[left(p)] + b[right(p)] - t;
      c[p] = c[left(p)] + c[right(p)] - t;
    }
  }

 public:
  SegmentTree() {
    st.assign(n * 4, 0);
    a.assign(n * 4, 0);
    b.assign(n * 4, 0);
    c.assign(n * 4, 0);
    build(1, 0, n - 1);
  }
  pair<int, pair<int, int> > query(int p, int l, int r) {
    if (l > r || l > y || r < x) {
      return pair<int, pair<int, int> >(0, pair<int, int>(0, 0));
    }
    if (l >= x && r <= y) {
      return pair<int, pair<int, int> >(a[p], pair<int, int>(b[p], c[p]));
    }
    int mid = (l + r) / 2;
    pair<int, pair<int, int> > f1 = query(left(p), l, mid);
    pair<int, pair<int, int> > f2 = query(right(p), mid + 1, r);
    int tmp = min(f1.second.first, f2.second.second);
    pair<int, pair<int, int> > ans;
    ans.first = f1.first + f2.first + tmp;
    ans.second.first = f1.second.first + f2.second.first - tmp;
    ans.second.second = f1.second.second + f2.second.second - tmp;
    return ans;
  }
};
int main() {
  cin >> s;
  n = s.size();
  SegmentTree st;
  cin >> m;
  while (m--) {
    cin >> x >> y;
    x--, y--;
    cout << 2 * st.query(1, 0, n - 1).first << endl;
  }
  return 0;
}
